Mouse Guard is Burning Wheel Lite, and that’s a very good thing. The Burning Wheel system is well-suited to Mouse Guard — it’s not an arbitrary choice in any way. The kind of game this system fosters matches up perfectly with the stories, tone, flavor, and heart of the Mouse Guard comic.
The core of the system is the same: You roll a pool of six-sided dice (no other types of dice are used), and each result of 4+ is a success; the number of successes is compared to the obstacle (difficulty) of whatever you’re trying to accomplish.
One area where the system really shines is in the ways you get and use bonus dice. Other players can assist whoever is making the roll by roleplaying out how an ability of theirs would be helpful, and granting a bonus die for their trouble; and your traits can come into play.
Traits have three levels; a level 1 trait lets you roll an extra die once per session; a level 2 trait gives you a bonus die for every applicable roll; and a level 3 trait allows you to reroll failures once per session.
I’ve played quite a bit of Burning Wheel over the years, and in actual play these elements of the system lead to a lot of roleplaying — and because most key rolls are stakes- or objective-based, rather than task-based, every roll really matters. That gets the whole table involved.