If gaming is your requirement then its not really worth upgrading that CPU to any CPU as the gains will only be slight or marginal. If you want to keep your setup consider upgrading your Graphics solution and/or adding a SSD is a fine little upgrade.
In general computing the FX 8350 will be a upgrade but I don't know if its exactly cost efficient at $200ish its still a higher price to pay.
I recommend keeping your cpu for atleast another year. It's not really letting you down is it? If so, have you tried overclocking it? If you've got the upgrade bug bad, how about building a cheap htpc or spare computer to tinker around with?
Well, the 965 BE is only 25% worse than the 2500k. Costs 50% less, too.
Also, with that motherboard, he could overclock the 965 to pretty high speeds, which will make the 965 as good as an i5 2500k @ stock.