Is there any difference in running an i7-3770K in a H67 chipset motherboard versus a Z77 chipset? Performance or otherwise? Does it waste that processor's potential?
I definitely wouldn't drop a 3770K into any H67 chipset. If you really are dead set on the H67, get a non-K CPU and you'll be good to go. Like others have said, the K would be wasted on such a board.
I tested 2600K on H67 and Z77/H77. With new chipsets Intel did something with iGPU utilization - same processor on new chipsets provides a higher 3DMark scores and higher iGPU overclock...
The only chipsets that will support overclocking of the 2nd and 3rd generation Intel® Core™ processors unlocked "K" processors are the P67, Z68, Z77 and maybe the Z75 (I am checking on this to see if I can get an answer on it). So I would stay away from any chipset that doesnt support overclock if I was looking to use one of the unlocked "K" processors.