The main one for me is expandability. The DVRs you get from your cable provider have whatever space they have - and that’s it. If you want to record more shows than you have room to store - you can’t. You have to start deleting stuff. With the WinTV - you can save as many shows as you’d like - and if you run out of room, just get an external hard drive and keep recording. You can also have and use this device if you already have a DVR - but say your cable-provided DVR only lets you record four shows at once - with a WinTV - you can record up to two more shows. Want to record even more - buy another WinTV, (and probably another computer - I haven’t tested to see if two WinTVs can run on the same computer or not - but I wouldn’t think so unless it was a very very powerful PC.)
Another advantage is exportability. The only way you can watch shows on your Cable-provided DVR is on a TV connected to that DVR (some companies are expanding it to any TV in your home, but you are still limited). Once the shows are on your PC from the WInTV, however, they are files on your computer - they can be exported to a different format and taken anywhere, on your phone, your tablet, your laptop, a DVD, whatever.
Now, for the downside - CableCARDs cannot do PayPerView or Video On Demand - so you won’t be able to watch or record those on your PC through the WinTV. Premium channels like HBO or Showtime work fine (as long as you are subscribed to those channels) - which some cable DVRs won’t even let you record.