The 3770K is clocked at 3.5GHz with turbo 2 up to 3.9GHz (stock)
The 3770S is clocked at 3.1GHz with turbo 2 up to 3.9GHz (stock) which probably accounts for its lower TDP of 65W
HD4000 is the same on both CPU’s but you can also overclock the GPU on 3770K
I haven’t run many benchmarks yet, but here is Cinebench with the 3770K at stock (5th entry)
The 3rd entry is the 3770K clocked to 4.4GHz.
The 3770K doesn’t get hot at stock speeds, and even the Intel cooler supplied will keep it reasonably cool, but a third party cooler will do better, and be quieter.
I think you have an Arctic Freezer 13?
If so, that would do nicely at stock speeds on the 3770S, and would probably allow an overclock on the 3770K up to about 4.2 GHz.