I've been to the falls twice, most recently in October where I based my stay on the Brazilian side. I would concur with those recommending a full day in Argentina's national park and a half day in Brazil's national park.
The Brazilian immigration officers did not stop us leaving or entering Brazil. My Brazilian guide/driver said that they usually don't stop Brazilian licensed cars with official tourist permits unless the driver is by himself.
For those of you considering a visit across the river into Ciudad del Este, Paraguay (which frankly is not worth a visit unless you are really into seedy border towns), Paraguay also requires visas of USA passport holders. You shouldn't try to travel outside of CDE unless you have such a visa and were properly admitted into Paraguay.