"쪽" is usually used to refer to "a specific direction", on the othe hand, "편(=便)" which is a Sino-Korean word is more like "to lean to one side(=쪽)".:) e.g. 오른쪽 >> the right side 오른 쪽 편 >> to lean to the right side, "not exactly the right side" \^o^/

As far as I can tell, 쪽 is more along the lines of side as in "east, north, left, right, right side window, left side of room". 편 is more like "im on your side" "the opposite side of the debate" "the other way of thinking things" "the other teams side".

another choice for 쪽 is 녘 but I do not think it is too common

Good question. I'd like to know the answer too.