YWZMatt :
Also, are there advantages to having more cores with newer games coming out?
Not necessarily, quad-cores usually suffice and are more than adequate; hence why i5's are often recommended for gaming. However games such as Far Cry 3 and supposedly Watch Dogs benefit from an i7's performance level rather than i5's, hence purchasing a CPU with better performance could profit you in that sense.
Games such as Battlefield 4 however does utilise Hyper Threading (HT), therefore you could benefit from 8 threads in total to offer you a more smoother game play experience. Not all games however utilise HT, but perhaps more in the future will.
YWZMatt :
Another question, what about the I5-3470? Is that better than the Xeon one?
No, the Xeon is superior and the i5 is inferior/weaker. I'd purchase the Xeon; it only costs a little more than an i5 but performs on par with an i7-3770.
The i5 is quad-core with no HT = 4 cores / 4 threads
The i7 is quad-core with HT = 4 cores / 8 threads
The Xeon is quad-core with HT = 4 cores / 8 threads
The Xeon is a better investment and you shouldn't need to upgrade your processor for quite some time, albeit Skylake (6th generation) should offer something new in 2015/2016.
All the best.