Lindy and West Coast are both 8 count dances, infact, west coast comes from lindy directly.

I've danced both, and I argue they're the same dance, but other people will disagree with me, but you still change your weight onto the same feet on the same counts in both, so that's my argument.

Interms of which style do you do? Normally east coast is associated more with Lindy Hop, than west coast. Lindy is traditionally done to classic big band and swing music, while West Coast is done to Pop and Blues music, that's generally at a slower tempo than Lindy.

Here's a link for the history of East Coast swing:
http://www.streetswing.com/histmain/z3ecs1.htm

history of lindy hop:
http://www.streetswing.com/histmain/z3lindy.htm

history of west coast swing:
http://www.streetswing.com/histmain/z3wcs1.htm