Background

I've been a TiVo fan for over 8 years, and I still use my Series-1 box in the living room even though I have MythTV working. I don't have a Series-2 or DirecTV TiVo, so any comments about those models are just from what I've heard, or from going to friends' houses and playing with theirs. I'm not going to include any functionality that can be added by hacking the TiVo.

I've been a Linux user and sysadmin for over 15 years, and I've been using MythTV since the 0.9 release, or about a year and a half. These comparisons are made using the currently released version, 0.19.

Summary Comparison

I'd say the TiVo wins in the ease-of-use category. You pull it out of the box, plug it in, and it just works. The only configuration issue you might have is getting the TiVo to control a cable or satelite box with the supplied IR-blaster. The interface is well thought out and easy to use.

MythTV definately wins in the freedom-of-use category. You don't have to worry about getting locked into propriatary hardware or software. The most common complaint is that MythTV is hard to setup and get working. This has some truth to it, as there are several prerequsite libraries and helper programs that MythTV uses to provide much of its functionality. There is a step-by-step guide that uses pre-compiled packages with a Fedora Core installation, that has helped many people called the MythTV on Fedora HOWTO. Another option is the KnoppMyth distribution which provides a bootable CD-image with a working MythTV installation.

Price

TiVo MythTV
Hardware Tivo has several packages to choose from, depending on how much storage space you want, and how much service time you want to pre-pay. MythTV is an application that runs on pretty much any hardware supported by Linux. You may even be able to use some extra hardware you have laying around. You will want some kind of video capture card and a video card with TV-out (if you plan on displaying it on a television). It's hard to set a price here because there are so many different ways of building a machine.
Software "Free". The Tivo software comes with the purchase of the hardware and the TiVo service. You have little control over what version gets installed on the hardware because it can get updated automaticly by the TiVo service Free!. The Linux operating system, MythTV and all its prerequsites can be downloaded for no cost and are distributed under the GNU Public License which affords the users and developers greater freedoms in how they use and distribute the software
Service TiVo has dropped the option of getting lifetime service; all the packages they offer have a monthly charge, which changes depending on how long of a contract (1 to 3 years) you want to commit to. The service provides software updates and program listings. A TiVo without service has most of its functionality disabled. "Free". MythTV gets its program listings via the XMLTV package or the DataDirect service from Zap2It. Both of these are free for now, but may not be in the future. Software updates are available for download for free, and only get updated when the user wants to

Basic Playback

Feature TiVo MythTV
Pausing/Rewind/Fast-forward Live TV Supported. Live TV can be paused up to a half hour before the buffer fills up Supported. The LiveTV buffer size can be changed by the user.
Pause/Rewind/Fast-forward Recordings Supported. Supported.
Skipping commercials Not Supported. Supported. When watching a show, the user can press a button to skip forward 30 seconds. MythTV also can automaticly find the commercials and notify the user or skip past them during playback.

Basic Recording

Feature TiVo MythTV
Single Recording by program Supported

You can choose a particular showing of a program to record.

Supported

You can choose a particular showing of a program to record, or choose to record that particular episode whenever it happens to come on.

Single Recording by time and channel Supported Supported
Recurring Recording by program Supported through their Season Pass feature.

Can record a program on a particular channel no matter what time it is on.

Supported

Can record a program when it appears in a particular timeslot each day, each week or any time on the chosen channel, or whenever the program appears on any channel.

Recording the show you are currently watching Supported. Pressing the record button while watching a show in Live TV mode will record the whole show, including any part of it you have already watched that is still in the Live TV buffer Supported. Same as TiVo.
Recording more than one program on at the same time Supported. The Series 2DT (recently released) can record two channels at the same time. Another option is to use multiple Series 2 boxes and schedule the recordings to happen on each box, then watch the recording on the remote TiVo using the Home Media Option Supported. One TV capture card is required for each simultaneous recording. Scheduling recordings on each card and handling schedule conflicts is resolved automaticly by the system.
Controlling a settop box (cable/satelite box) Supported. Choose your model of settop box from the list of manufacturers. Can control settop boxes by either a serial cable or the supplied IR blaster. Supported through the lirc package for settop boxes without a serial port. The package comes with configuration files for many types of remote controls, or you may have to create your own configuration. For settop boxes with serial ports, MythTV includes channel-changing programs in its source archive for some Motorola cable boxes, and programs for other types of boxes can be found on the Internet. For STBs with active firewire ports, MythTV can use that conenction to change the channel.
Identifying Duplicates When scheduling a recurring recording, you can choose to record only the new episodes, or both new ones and the re-runs. Duplicate recordings can be identified (and not recorded) by a combination of shows that MythTV has recorded any time in the past and current recordings stored on the disk

Digital Television

Feature TiVo MythTV
Record and play back digital cable channels Not Supported directly. Recording digital cable channels requires the use of the cable company's STB. Supported. Capture cards such as the HD-3000, Air2PC or Avermedia cards can capture non-encrypted QAM encoded channels. Depending on the local cable company, many or most channels will be encrypted, and require the use of a STB.
Record and play back HDTV terrestrial broadcasts Not Supported Supported with several cards, including the HD-3000, Air2PC or Avermedia cards.
Record and play back HDTV satelite broadcasts Supported. DirecTV customers can purchase a satelite receiver+TiVo box that can record and play HDTV channels. That particular box can also capture terrestrial DTV broadcasts Not supported The best you can do is record the SD resolution picture output by the STB's composite or Svideo connection.
Record and play back HDTV cable broadcases Not supported This feature is expected when the Series 3 box is released. Supported with some caveats. For Motorola 6200-series boxes with firewire ports, when the local cable company has chosen to activate them, and when viewing a channel the cable comany has chosen to allow to be sent unencrypted over the firewire.

Searching for shows to record

Feature TiVo MythTV
Search by Title Supported. Titles are entered by selecting the first few letters of the show's name on a virtual keyboard on the screen with the remote, and then selecting the right one from a list of shows matching that pattern. Supported. Titles are selected by choosing the first letter of the show's name and then scrolling through all the shows starting with that letter to find the one you're looking for.
Search by Genre Supported. The TiVo interface can present a list of genres and subgenres, and allows searching for titles limited by the genre you select. Supported. The user can select from a list of genres (categories), and then choose a show from the list of shows in the selected genre.
Search by time and channel Supported. The TiVo has an onscreen guide where you can select a channel and see all the shows coming up for the next several hours. It also has a familliar TV Guide-like time/channel grid to select shows (Series-2 only). Supported. It has a TV Guide-like time/channel grid to select shows.
Automatic recording of similar shows Supported. TiVo uses anonymous, aggregate data from its subscribers which allow it to record shows similar to the shows the user has selected to record in the past. Not Supported. An add-on to MythTV was under development at one point.
Search by criteria Supported through their Wishlist feature. You can select shows with some combinations of actors, directors, genres, titles etc. The Wishlist feature also allows the user to schedule a recording that isn't actually in the upcoming program list yet. Supported The user can put in what amounts to portions of an SQL where clause to match shows in the Program table.

Living on the network

Feature TiVo MythTV
Remote access to the user interface Not supported Supported. Since the interface is just another X application, you can remote-display it to another terminal. Video can not be played back in this way because it uses the Xvideo extension, which requires local access to the video card.
Scheduling recordings over the netwok Supported. Series-2 TiVos with the Home Media Option can schedule recordings through their account on the TiVo webpage. Schedule updates only happen when the TiVo makes its daily call for the service update. This is not supported on the older Series-1 TiVos. Supported. An add-on module called MythWeb allows the user to, among other things, schedule shows to record. These changes are scheduled immediately.
Playback of shows recorded on a remote device Supported. Series-2 TiVos with the Home Media Option, and that are in the same household, can play back recordings made on another Series-2 Tivo. Supported. Because of MythTV's client-server architecture, all recordings are essentially remote to the frontend that plays them back. This architecture allows the user much greater flexibility in deploying backends (machines where the recordings take place) and frontends (where the playback happens), possibly multiples of both types of boxes.
Storing and playback of recordings on a remote fileserver Not Supported Supported. Since MythTV runs as a normal application on a Unix machine, any of the available network filesystems can be used to provide remote storage
Moving recordings to another machine or burning them to disc Not Supported. There is a TiVo box that supports burning recorded shows to a DVD, but it is more expensive then the basic television-only box. Supported. Recordings captured with a hardware mpeg card such as a Hauppauge PVR-250 are normal mpeg recordings saved to the filesystem, and can be moved and processed with any program that supports it. Recordings made with a bttv card are made in a MythTV-only modified NuppleVideo format, but are still normal files that can be moved around. There are patches for mplayer to understand this format, and another program called nuvexport that can translate these files into other formats such as svcd images or xvid files.

Playing other types of media

Feature TiVo MythTV
Playing DVDs Not supported. There is a TiVo box that includes a DVD player and recorder, but it is more expensive than the basic television-only box. Supported. Playing DVDs is accomplished by calling another program that supports DVD playback such as mplayer or xine. Once it is configured, the MythTV interface can call that program without additional user intervention through the MythDVD plugin.
Ripping DVDs Not supported. Supported. The MythDVD plugin provides an interface for calling another program that does the actual ripping.
Playing other computer video media (.avi, .mpeg, etc) Not Supported Supported. Playing other video media files is accomplished by calling another program that supports their playback such as mplayer or xine. Once it is configured, the MythTV interface can call that program without additional user intervention through the MythVideo plugin.
Playing Music Files Supported. Series-2 TiVos with the Home Media Option can play back mp3 files stored on a MS-Windows computer elsewhere on the local network Supported. The MythMusic plugin supports playback of mp3, ogg and flac files on the local machine, or mounted as a network drive.
Ripping Music Files Not supported Supported as part of the MythMusic plugin
Displaying pictures Supported. Series-2 TiVos with the Home Media Option can display picture files stored on a MS-Windows computer elsewhere on the local network Supported through the MythGallery plugin.

Other Features

Feature TiVo MythTV
Integrated Web Browser Not Supported Supported through the MythBrowser plugin.
Browsing news headlines Not Supported Supported through the MythNews plugin.
Local weather reports Not Supported Supported through the MythWeather plugin.
Playing Games Not Supported Supported through the MythGame plugin. It supports calling another program such as mame to act as a video game emulator.
Video Conferencing Not Supported Supported through the MythPhone plugin.

TiVo, Season Pass, Wishlist and probably some other terms are trademarked by