To not rush, and to be able to really take in the spectacle, you should consider taking a large part of a day to visit Iguazu Falls, on either side. With this, I'm saying that you shouldn't try to visit both sides on the same day.
But, visiting the falls on the other side is very easy. You can take one of the many regular public buses that travel between the two towns on either side and go from there.
The real difference between the two sides isn't that big: On the Argentine side, you get very close to the top of the falls, on the Brazilian side, you end up on a platform that's pretty much surrounded by walls of waterfalls. Both are impressive.
When pressed, some tourists, who have visited both sides, think the Argentine side might be a bit more impressive, but, from my experience, those that visit both sides, more often than not, start on the Argentine side.
However, there's another reason that might make you want to visit the Argentine side, if you only want to do one side: With the struggling Argentine peso, exchanging USD in cash can get you a huge discount in practice. I'm not sure what the current 'blue rate' of the USD is, but, last year, the difference was as much as 40%, meaning that if you brought cash USD into Argentina, you basically got a 40% discount on everything (if you were willing to change your USD on the street).