Ok, with people, the distinction is quite clear. You can only use odwiedzać. In most other cases both verbs are possible, and the difference is quite nuanced, I'd say. Zwiedzać is closer to tour around, and odwiedzać is closer to visit. You can of course say zwiedzamy muzeum, the meaning wouldn't change a lot. It sounds, hm... more thorough, maybe?
However, if you say "zwiedzam Francję", that would imply that you visit more than just one place in France, but "odwiedzam Francję" can theoretically mean that you just take a look at one specific place and leave soon afterwards.
"Zwiedzać" = visit, tour, see, perambulate, inspect.
"Odwiedzać" = visit, go, see, call, pay a visit, pay a call.
You can "odwiedzać" not only people but also familiar places, especially the ones you used to live in ("odwiedzać stare kąty"), like a district you used to know very well. The goal is to refresh or bring back memories. Rare usage: we also go somewhere to spend some time there, even for a new place.