On both sides, you’ll buy your ticket then need to take some form of transport to the falls themselves, as the ticket offices are located some way from the main attraction. On the Argentinean side, you’ll catch a train to the Devil’s Throat, a narrow chasm where about half of the water falls — there are also many other smaller falls spread out over a 2.7km stretch. On the Brazilian side, you’ll travel by bus to the same location, though you can get off earlier and walk along the river for panoramic views.
On the Argentinean side, you’ll see the Devil’s Throat from above, in Brazil from below. The Argentinean side offers other walkways as well, such as the Upper and Lower Trails, while Brazil has just the one path.
Each side has something to offer and it’s highly advised that you visit both. Just don’t forget your raincoat!