Brazil: less than 1/3 of the falls, some great views and a boardwalk, the Dos Cataratas hotel, possible helicopter rides, a natural history center you can see caged fauna of the area - and in the Cataratas area, very aggressive coatimundis that will fight you for food (and win) or happily rifle your backpack for any morsels you might have in it. You can do it all in a few hours.

Argentina: 2/3 or more of the falls, many hikes including to an island with great views, boats into the throat of the falls, fauna you can see (especially a rich avifauna) in its natural habitat (especially if you're at the Sheraton and go out before and after the day hordes arrive), boardwalks out over extensive parts of the falls, excursions into the second growth forest. It will take two days to really experience the falls. (No helicopter rides from this side.)

I've done both. We stayed at the Sheraton and as we had Brazilian visas did a day trip to Foç. Definitely, if you're already in Argentina, visit the Argenitine side - for a couple of days if possible.