Well, the Broadway cast stays in New York and does Rent at the Nederlander Theatre. The Broadway cast is also part of the Actor's Equity Association. The tour cast travels all over the country, and the actors are not Equity.
The show is exactly the same if you see it on Broadway or tour, besides the cast, and a few lyrical changes here and there. (For example, in 'Happy New Year', when Mark sings "You can take the girl outta Hicksville, but you can't take the Hicksville outta the girl" they replaced Hicksville with Jersey because they didn't think people in the rest of America would know where Hicksville is.