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. :)
You can actually do some really cool low-magic / low-power games with Burning Wheel there is a pretty good let's play channel (can't recall the name, think it's Patronage) that uses Burning Wheel to explore the players as artisans in a Renaissance analog.
From what I understand, a big difference of BW compared to a lot of fantasy is that it is fantastic at character forward play, with the game looking like a series of vignettes with each character as opposed to a singular scene of the adventuring party. Which can be great when you want to do a political intrigue a la GoT where one player is a magically inclined daughter of a farmer, one player is the bastard son of the corrupt and ailing king, and the third is a veteran captain of the guard to the king. With BW, you can have each character's Beliefs / Instincts help guide the game towards the ascent of the bastard to the throne, but for a good chunk of the game each player's "scenes" may not connect the other players. Some good advice I've seen on this is to have the players whose characters are not in the scene actually RP the NPCs, which I've yet to do but sounds great in theory.
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!