The 660 has a higher core speed and memory speed. The R9 270 has a higher memory bus and more memory bandwidth and more shader processing units. Technically they both have their advantages over each other in different areas but from a consumer standpoint i would say go for whichever is cheaper. They are both pretty balanced with the R9 270 probably performing slightly better in most situations.
EDIT: i was looking at the R9 270 not the R9 270X, the 270X is a bit better then the 270, they are still pretty balanced cards though the 270X probably would come out on top.