Advance MAME is the best choice all around... it outputs perfect display that matches the original arcades.... you get perfect display at correct refresh
Advance Mame is designed only for some graphics chipsets, but many are supported... and of course Euro SCART TV is even better then an arcade monitor, and most importantly much much cheaper...
You have to solder you VGA to SCART lead by yourself though...
Xbox MAME currently is very limited:
1) it does not output correct diplay at all - you can either use some fixed resolutions like 640x480, but the image doe not cover the whole screen like it should, or you can STRETCH the image, but again it is not the correct display, since stretching messes up pixels (some pixels are missing etc. - it can be seen in XSNES9x when point filtering is used); and lastly that BLURR effect used in XMAME (probably to mask incorrect pixelation in stretching) spoils the authentic look, mainly of the older games like Moon Patrol, Galaga... that games should look sharp and bright, not like on a 20 years old worn out TV screen... I simply cannot admit that blurr effect is good, it spoils the quality of the display and I do not like it at all
2) it only support 60 Hz games correctly - because TV screen (NTSC) refreshes only at 60 Hz and because Xbox is designed to output NTSC signal (only 60 Hz) there are many many games that cannot be run properly on Xbox MAME. For example Smash TV should be runon 53 Hz display... Do Don Pachi should run at some 57 Hz I guess.. if you run those games on Xbox, you will either see jerky scrolling / movement / animation or if you enable VSYNC in the INI file, you spoil sound that would still tend to go at original 53 Hz... the only sotuion is to get 53 Hz screen and it is not possible with NTSC TV (well, Euro SCART TVs are capable of diplaying 50-60 Hz but I do not have the idea how to fix this with Xbox, and why would anyone bother doing that when you can hook up powerull PC and Advance MAME to this kind of TV...; Americans are limited and should opt for Arcade monitors intead, we in Europe have the cheaper choice with those TVs)
3) of cource 733 MHz CPU speed and 64 MB RAM are also limitations for some more complex games from 90's (especially)
conclusion: buy Xbox for next generation gaming, build your arcade PC for classic gaming