I've seen 4 billion (heh) element roof antennas pick-up very little, and loop antennas receive full strength. So it's really trial and error without knowing how good the reception is where you live.
If you get something (if not much) with a set-top antenna, a roof antenna might be just the ticket. I used a roof antenna for a while and the picture (being uncompressed) in HD was certainly better than via satellite or cable.

Sig' begineth here: