FWIW, both TiVo Seires 3 (which has superior OTA reception compared to all subsequent generations of TiVo) and Dish's built in (although perhaps NOT 612; that was a buggy odd bird of a box), or modules had the same VERY GOOD performance. I have both Dish and TiVo connected to the same OTA antenna. No question that all my TV's perform BETTER than any of the TiVo's or Dish products, but that is generally the rule, probably because TV makers/brands see the OTA tuner performance being more critical and among core functions, even if majority of TV owners never use the OTA tuner built in the HDTV.
I believe TiVo and Dish (Echostar) used the same manufacturer for their OTA tuners.
TiVo Premieres (S4) OTA tuners became legendary for its VERY poor performance, certainly when compared to the previous version S3 TiVo's. Subsequent Roamio (S5) TiVo's OTA tuners IMPROVED from the horrid S4, but still NOT AS GOOD as the old S3 TiVo's. I do not own any TiVo Bolts (S6), but from what I gather on the TCF (TiVo Forum), while the Bolt seems adequate, it is still inferior to the now 12 year old TiVo S3 models.
My TiVo S3's get the most channels with very strong to good signal strength, and over the years and still today, all Dish OTA's performed nearly IDENTICAL to the lauded S3 TiVo tuners. Only the TV's manage to pull in a few Low Power stations that neither TiVo S3 nor Dish can do. However, all TiVo models OTA tuners later than the S3 perform worse to varying degrees, while all the Dish OTA tuners I've used over the years have performed equally as the TiVo S3.
As of today, TiVo S3 OTA and Dish OTA (including single and dual tuner dongles) perform just as great as the TiVo S3 OTA tuners. Overall, the dish OTA tuners are very good--HOWEVER, I believe most of the problems people are having that I've observed have to do with multi-path, and while some OTA tuners can deal with it a little better than other, mulit-path is a well documented MASSIVE flaw of ATSC with alternatives of the day, including DVB-T, being far less susceptible to multi-path. Anything less than very good OTA tuners are not going to perform nearly as well, and only the TV makers/brands are willing to spend the most money for what are probably the BEST OTA tuners out there. Our OTA TV system should be (should have been designed to be) able to allow "very good" and "good" OTA tuners to work "very well" (not quite the level of Excellent for the best OTA tuners), not the situation we have today with ATSC 1.0.