The falls are spectacular from both sides. 70% of the falls are on the Argentina side, therefore you are going to see more of them from the Brazilian side since that faces them and they have a series of catwalk trails. The boat trips go from the Argentine side.

We stayed on the Brazilian side since we were on a trip to Brazil at the time, but took a day trip over to the Argentine side. Although you need a visa for Brazil, if you go on an organized tour over to the Brazilian side they probably take care of that via some kind of group visa.

And as Fred recommends, do watch the Mission before you go - while we were there I kept hearing the music by Ennio Morricone running through my head.