Owning a Series 3 (the original THX with the OLED display) and seveal Dish DVR's, Dish DVR's are better. However, I would say that Tivo is a good product. Dish DVR's can record up to 4HD channels at the same time. While Tivo can record both QAM and OTA, it is still limited to only 2 HD recordings at the same time. Some more differences:
Dish has PIP, not Tivo; Dish has video and audio in most of the menus, Tivo does not; Dish better guide display and the extended display is also offered and better (subjective, of course); Dish buffers for one-hour; Tivo Series 3 (all models) only buffer for 1/2 hour; Dish larger HDD or just more capacity (remember Dish is MPEG4 unless OTA); Dish better external HDD solution allowing unlimited number of HDD's and that can be connected (although one at a time per box until software update) to any ViP boxes on your account, from one to another to another, etc., which means you can have 1TB HDD for movies, another for TV, another for the wife, another for the brats, and they can be connected to any of the ViP boxes on your account and you can switch and change them around while Tivo limits you to one external HDD that is "married" to that DVR and must always be powered on or you may lose all your recordings (no we do not count any hacks in this game); Dish menus much LESS cumbersome; DHHP warranty will replace DVR at no cost and no rip-off of the "Lifetime membership" up front $$$ robbery. Tivo really hoses its subs on that one (I have come across several Tivo subs who have had extremely negative experiences regarding their "Lifetime" membership); Dish has less expensive DVR monthly fee.
Now, Tivo does have the most aesthetic interface. The displays are all very large and clear large sized fonts and very pleasing backgrounds that are all easy on the eye for its menus and list of recordings and all except the guide which is not as good as Dish's. Also, I love the OLED display (not available on the HDXL nor HD models) of what it is recording because when I see the red light on Dish, I do want to know what is recording without having to turn on the TV. Tivo has the most robust search features with far more categories of individual sports than Dish and more categories in general. Tivo does have the best access to a wide variety of content available on the web. Options include Netflix, Amazon large library and several other content such as The Onion.
While Dish DVR's are still, overall, the best out there, it is clear that the Tivo is far superior to any of the cable company DVR's or AT&T Uverse or FiOS DVR's. If I left Dish, I would probably invest in Tivo boxes. However, if it were OTA only, I would probably go with the DTV Pal DVR by Echostar (Dish Network) because while it isn't as "sexy" as a Tivo, it does the same job with NO monthly fees at all and has the same external HDD solution as the satellite boxes. The latest firmware update for the DTV Pal DVR seems to have fixed some earlier issues and now that the conversion has occurred, more accurate PSIP has made guides reliable.