The main difference (and reason for increased price) is that the 8700k makes use of hyper-threading. Therefore, the 8700k has 6 more "threads" compared to the 8600k. Also, the 8700k has a slightly higher base frequency but a decently higher turbo frequency.
As for gaming, both CPU's are decent and will get the job done. The 8700k will do the job better, but it'll cost you a fair amount to make the increase. For a decent comparison, check out userbenchmark.com. There's quite a few sites that give stats for both of these CPU's if you want to make more comparisons.