Asking this question here should get you an enormous bias to
TV3.
I have both. For quality of picture, quality of sound and pricing of 1080p content, BD wins hands down.
For ease of use, it depends on the UI of the BD players you are considering. I thought the UI for the final incarnation of
TV gen 1 was excellent but since then Apple has made decisions that reduce the intuitiveness. For example, back then, my own movies would be found under "movies", my TV shows would be found under "TV shows". Now those same headers still exist but all personal content shows up under "Computers."
iTunes Extra is a weak incarnation of something like extras on discs. Hardly anything has iTunes extras and I don't believe- someone correct me if I'm wrong here- that
TV3 even works with iTunes extras at all. Personally, I think iTunes Extras is like Ping (days are numbered though it still technically exists).
So relative to just your bullets, I'd say BD (and I own
TV3). The big win for
TV (besides the importance for so many that it is made by Apple) is the convenience of content availability via the iTunes store. Netflix & Hulu is generally available on BD players too so I null them out. If you are going to rip your own collection of BDs for
TV3, you have even more ready access to your movies (no waiting on the downloads).
All the said, if you don't have any real experience with
TV, it is a great device. While it still has a ways to go to get fully toe-to-toe with BD in terms of picture and especially sound quality, it is also an iTunes music jukebox, podcast/vodcast player, internet radio, photo collection on demand on the big screen, etc. For $85-$100, I'd buy it solely for the iTunes jukebox functionality (I remember it wasn't that long ago that I would lay out several hundred dollars for a CD jukebox player).
1080p from BD rips or iTunes does look very nice but not quite as good as BD if you are able to see the finer details on your setup (of course, others will argue "'I' can't see the difference" (so apparently you can't either). Sound is capped at 1992's Dolby Digital standard vs. the much more modern, richer audio alternatives support by the BD standard. Again, fans will likely argue "I can't hear the difference" (so you can't hear it either).
Jobs called BD a "bag of hurt" so here it is definitely a "terrible", "obsolete", "on it's way out", etc technology. But Apple still hasn't delivered something that is toe-to-toe on the most important variables it delivers. If that really matters, you need to move toward Mac Mini and maybe Plex or similar.
And one last thing: you own a BD collection. You have a lifetime-but-"nontransferable" license to any iTunes media you buy. You could sell your BD collection later on to others and they could get full use out of it as the new owners. You can't sell your iTunes media purchases to others. You can will your BD collections to various loved ones when you die. You can't really pass on your iTunes media to others in a similar way (the concept of just giving them your iTunes account info is a very poor substitution that is very commonly argued as if it is almost as good). This may or may not matter much to you but it is the reality of things as is.
I expect about 90% of any other feedback you get to bash BD in favor of Apple because you've posted this question here. I own lots of Apple stuff myself but I've offered you the objective feedback above.
