Mame as far as I know, currently only uses at most 2 cores.
The speed increase from turning on multithreading (using 2 cores instead of one) is about 5%.
There is zero additional benefit to having 4 cores, since Mame is not programmed to utilize them. You could see a slight increase if you managed to push all other computer processes (of which there shouldnt be many anyway) to the 2 cores that Mame is not using, but I wouldnt expect that to be a noticable difference at all.
Its possible that in the future Mame will utilize multiple cores more, and better, but due to the nature of emulation, thats not likely at least for a good while.
I would imagine the E2180 would be matched up fairly well with the P4, maybe even slower. If you are trying to keep your budget down, I would go for the E7200, $119 at Newegg, and should smoke the E2180 in Mame.