The classic xbox is the equivelent of a pentium 2 machine with hardly any ram. In regards to mame, it performs about as well as a pc with said specs (in other words not so great).
There are other emulators for specific types of arcade games on the xbox (neogeo, cps2, ect). These perform better than mame, but again, the xbox doesn't have a lot of ram so even with the extra help many games won't work due to their sheer size, neogeo in particular.
Their might be a compatability list somewhere.... google is your friend.
The last year or so in the xbox's lifespan I had mine modded and played mame and the like on it. I loved it at the time. However, as soon as the 360 and wii came out I boxed it. Why? The thing is huge, loud, and at this point doesn't do anything that I can't get my wii or 360 to do. (Media streaming on the 360 and emulators on the wii). On top of that I actually get use out of my 360 and my wii has roughly the same specs as the xbox only it's quiet and the size of a cd drive.
I guess my point is only use a xbox if you don't have anything else or you have a special project in mind.