I agree with using an older PC, like a Pentium 4 or Core 2 Duo (or the AMD equivalent). I wouldn't touch an original Xbox with a ten foot pole, at least if MAME/MESS is being considered as one of the emulators. That said, they seem to do OK with the classic console emulators like the port of Snes9x - but so does my 1.2GHz Celeron from 2001, which was also quite happy playing anything up to UMK3 (the last MAME build used on that PC was 0.89, after which it was replaced with a new PC). Also, old PCs are practically thrown away whole these days, so they will be much cheaper than buying an Xbox and all the necessary parts. Also, Xbox controllers.
A late model Pentium 4 system wins hands down over an Xbox/Android (and blows away a Raspberry Pi), just avoid the Prescott CPUs if you can't keep them cool, e.g. SFF case or poorly ventilated cabinet. Hot internals will eventually lead to fried capacitors, which will eventually lead to a fried power supply or even the mainboard itself (bonus points if the PSU is a cheap one with all the power on the 5V rail and no guts on the 12V). One question though, does Microsoft still allow people to validate XP?