Speaking from experience, the Xbox emulation present on the 360 SUCKS. 😜 The compatibility is poor, and some of the games that do work run really slow and/or choppy. Hell, Halo 1 in its cooperative mode even runs pathetically, and not only was that one of the games the emulation was supposed to be optimized for, but it was also a launch title on the original Xbox, so it shouldn't be that demanding. 😜 I should also point out though that I was playing this on a 720p TV, so that might have something to do with it.
Conversely, I played a splitscreen deathmatch on Halo 2 a loooong time ago when my cousins just got their 360 (this was before Halo 3 came out), and I actually remember it running just fine, though this was on a standard definition TV. As well, I recently tried Burnout 3 on my 360 with my 720p TV, and that ran well too, though it's not that surprising considering that it was a multiplatform title likely developed mainly with the PS2 in mind. 😜