compared to the $400 Nikon D3100, which one is better?
6, half dozen. Both are very good entry level cameras. I'd say go with what you or your friends have already. For instance, I have a Canon 60D, 24-105mm, 50mm f/1.4 and if I had a really good friend who I really trusted a ton, i might let them borrow a lens. Maybe. Otherwise, if you don't have any initial brand loyalty, you can't really go wrong with either.
Having a great time and visiting family are mutually exclusive.