What makes it your favorite? Do you want to play it? If so, what's keeping you from doing it?
For me, it's Burning Wheel.
I bought it purely based on aesthetics back in 2008ish, then got the supplements, then Gold, then Gold Revised, with the Codex, and the anthology...
I blame it for my weakness for chunky, digest-sized, hardcover RPGs. :P I also like the graphic design, I like the prose (even if it's divisive), and it has both interesting lessons you can plug into other games (like "let it ride," letting success or failure stand instead of making lots of little rolls) and arcane systems that pique my interest (like the Artha cycle, which makes roleplay, metacurrency, skill rolls, and advancement all intersect). I genuinely like reading it for its own sake.
I haven't played it because... well, since it's not D&D, that immediately makes it harder to get people interested, sadly. It's also a bit daunting, given its reputation as a crunchy system. But I have a group of players interested in trying new things, and fewer other games calling for my attention, so hopefully I'll get a chance soon. :)
I'm not an expert on the three either, but here's my understanding:
Burning Wheel is the oldest of the three, the most complicated, and geared towards dramatic fantasy stories. It's replicating classic fantasy novels and the like.
Mouseguard came out next, is significantly simpler, and obviously made to evoke the feeling of the comics it's based on.
Torchbearer is the newest of the three, is an intermediate level of complexity, and geared towards dungeon crawling and the like. Think old-school RPG with a Burning Wheel chassis.
I still haven't got my hands on Mouseguard, and I'd love to try all of them at some point. It just breaks towards Burning Wheel for me, to begin at the beginning—but they all have a unique appeal. :)
@Lianodel @pikasaurX4 I own all three and have played one con slot of Torchbearer of which I remember none of the interactions with the mechanics, and pretty much none of the story.
I did find a Burning Wheel LP with that name, so I'll have to check it out!
There's also a podcast I loved called Campaign, and since a lot (all?) of the cast were improvisers, they would hop into scenes as NPCs quite often. (I'm pretty over that podcast, but when I liked it, that was one of my favorite parts.) I tried that in other games, but it was a bit hard to get non-improvisers to get into it. I'll have to try again!