The i3 is significantly faster per-core (don't compare clock speeds here, meaning the gigahertz [ghz] number, different platforms have varying IPC - instructions per clock), though the AMD chips can catch up with skill, effort, and higher power use through overclocking.. The i3 also isn't a true dual-core. It has hyperthreading, which helps out a surprising amount in games that can use 4 threads. Overall, I'm a gamer, and the i3 has equivalent or superior performance to an overclocked "quad-core" if by "quad-core" you mean an AMD Phenom II x4 or fx-41X0, especially in games that are CPU-bound like StarCraft II and Skyrim, and which I also play. And because of the way games are programmed, per-core speed is much more important than total CPU potential. For instance, SC2 can only use two cores, so the fastest two cores possible is what you want. Skyrim can use basically two cores, but really only the first is heavily taxed, so again, the highest per-core speed is what you want. Other 'multi-threaded' games show a similar bias - because of the way games are programmed usually only a few cores are heavily taxed - and these are the ones that limit your performance.
Don't get me wrong, AMD would be great if you were both gaming and doing some other multi-threaded task. Although in that case I'd recommend an fx-6xxx. And a stronger PSU. Don't use the cheap PSU I recommended if you plan on overclocking an AMD chip. Though the fx4100 would be ok on it, I guess.
But the kicker for a gaming situation is simple: the i3 is cheaper, and allows for a better video card. Combined with not sacrificing performance, and I don't care if it's single-core, I like better performance for the same price or cheaper.
P.S. Copied from another post:
Note those games above are CPU-limited games. Most games couldn't care less which processor you put in your computer.
Edited by MisterFred - 8/20/12 at 10:37am