Why not both? My basement is perfect, half finished (rec room w/ ping-pong, darts, couch etc) and the other half unfinished (floor to ceiling storage shelves).

Works great for me, got pretty much unlimited storage, plus a place to hang out. Only downside is no bathroom or bedroom down there, but that'll only ever be an issue if we have 3+ kids, at which point we'd probably be looking for a bigger place anyways.