The OP has one of those REALLY OLD Series 2 (SD only) DVD burning units. They were released about 10 years ago. They were discontinued AGES ago. Although it sounds nice, the transfer to DVD INCLUDES the commercials (TiVo has always brown nosed content owners) and lacks all the power and features of a true DVD recorder such as editing among others. I can playback my Dish content to my DVD recorder with internal HDD at high bit rate, and easily edit OUT the commercials. Those DVD burning TiVo's were very expensive when they came out and just didn't sell, but I understand the appeal when they first came out (with a diminished, but FREE and almost useless TiVo Basic service level that was a VCR experience, but if you wanted the functions that really matter like Name Based recording, Season Pass, Kid Zone, Wish List, all the powerful search features, and more than 3 days of guide data, and other "Smart" features, then you had to pay extra per month for the full TiVo Plus service), but I became disinterested when I learned one could not eliminate the commercials. I can fit multiple episodes of TV shows on one DVD5 at high to good bit rate by removing the commercials that allow for more content. This a Standard Def TiVo ONLY.
There is a way, however, to record TiVo content from a Series 3 (High Def) or Series 4 (Premiere [High Def]) over to a DVD: PLAYBACK the content in REAL TIME connected to a DVD recorder, just like one would have to do with Dish.
Oh, except on my Dish box I can set it to DUAL mode and playback to DVD on TV2 while I watch different content on TV1 at the same time. Far nicer than losing all playback function of my TiVo when I want to dub content to DVD, so Dish wins there. And with a Joey, it would have the same or even better flexibility for dubbing that TiVo does not. So, no, one is not necessarily better than the other, for at least the last 10 years!
