i7 3770 vs i5 6600

If you have a 1155 motherboard just stick with it. Unless you need things like NVMe SSD's, DDR4 which honestly you won't see a huge difference with, or worried about conserving energy just stick with the 1155 i7. There is still life left in that guy. if it was a 3rd gen i3 i'd say upgrade but 3rd gen i5 and up are still good for gaming.
 
Agreed.
If you're buying new get the 6500 over the 6600, as the price difference is quite a bit, and the performance difference is tiny.
If you currently have a 3770, you'll have better performance in multi-threaded applications and about the same in others.
No need to worry about upgrading.
 
Both cpu's will handle everything you throw at them.
Since you have a LGA1155 already the i7 3770 is your best bet and will last you multiple years. It will not bottleneck any card out there. :)

I have an i7 4790, the i7 3770 is only 5-10% behind it in raw power, I have my I7 paired with a gtx 1070 and they have no issues with any game ive played so far which are, Battlefield 4, Battlefield 1 beta, sw Battlefront, witcher 3, DOOM, far cry primal etc.