Hello and welcome to the forums
It depends on your budget and usage.
The main difference between them is that socket 1136 motherboards usually have better OC'ng potential, support 6-core CPUs and have 2 PCI-E x16 slots;whereas, P55 boards don't support 6-core CPUs and have 2 PCI-E x8 slot but they are cheaper.
Your subject is LGA1366 vs LGA1156 and you question is what is best with a Core i7 - are you asking which socket works best with an i7? Or are you asking what the differences are between the two sockets?
If you're asking which socket works best with an i7 - well there may be some confusion that needs cleaned up. An i7 8xx only works in socket 1156. An i7 9xx only works in socket 1366.
If you're asking what the differences are between the two sockets, well others have answered this already. 1366 allows for triple channel memory, while 1156 brings the memory controller on die. 1156 integrates PCI Express and the DDR3 memory controller.
There are hexa-core processors that will run in 1366.
1366 is rated for memory frequencies up to 1066 MHz while 1156 is rated up to 1333 MHz - although each can run RAM OCed much higher.
1366 supports 2 PCI-E x16 slots while 1156 can support 2 PCI-E x8 slots. In testing this has proven to be a noticable difference only when running SLI/CF on the highest end cards.
1366 is typically more expensive, runs hotter and takes more power. However there are $300 1156 motherboards that will quickly eat up any cost difference.