I finally picked up The Burning Wheel yesterday and read the first 77 pages before bed. At that point Luke tells the reader to go read the Character Burner, get some friends, make some characters, and try out the system as presented so far.
Burning Wheel is a pretty heavy system, so I like that the core is separated out like that. It means that there's a natural way to introduce players to the system. The Battle of Wits, Fight!, and other rules can be introduced later as players master the core concepts.
The other major impression is that the core concepts are subtle but powerful. Nowhere does Luke say that gameplay involves very large chunks of time resolved with some narration and a scant few rolls. If he had, the reader would probably rebel (if they're a very D&D-style, moment-to-moment gamer) or would have a hard time reconciling that high level of task resolution with the fine-grained character system. Presented as it is, though, the idea that infiltrating the Prince's castle and absconding with his valuables can be resolved with a few linked tests in a matter of minutes of play time—and that this is a good thing—just arises naturally as I grasped the mechanics and read the examples. I'd read that Burning Wheel games get a very lot done in even short sessions, and I can see why now.
The drawback and strength of the system is how much decision power it puts into the players' hands. It doesn't just say that the game revolves around the characters, but it actually builds it into the fundamentals of the rules. If you're using The Burning Wheel, you can't not make the game turn on the characters' choices.
How is this a drawback? The system demands very high rules contact from the players. Unlike a number of other systems, you can't run The Burning Wheel for players who don't care to ever learn the rules. Consciously handling the rules is the only way for players to make their characters effective at tasks. Some systems will work fine if the players just declare their fictional actions and leave translating that into mechanics to the GM. The type of gameplay it offers that distinguishes The Burning Wheel from other systems is inaccessible to that kind of player. There's little point in playing The Burning Wheel without investing heavily in the system as well as the characters and world.
I can't even say that the handling time for the system is long or short. It seems as if the system is almost always being handled. The system being very intertwined and about as elegant as such a heavy system can be will make handling the rules a pleasure, though.