I started off on the Brazil side. If you do spend a night there it needs to be at the Hotel das Cataratas. It's inside the park so when the park closes and the tourist go home it's all yours, same for in the morning. You can go out before the first bus arrives.
Just outside the park on the Brazil side there's a bird park. Worth a stop if you like birds. There's also a large hydrolelectric plant.http://www.tripadvisor.com/Attraction_Review-g303444-d318113-Reviews-Itaipu_Hydroelectric_Power_Plant-Foz_do_Iguacu_State_of_Parana.html
I didn't get to the hydro plant but flying over, it looked amazing. The river was flowing a lot and the spillway was just massive, going down and then ramping up into the air.
I preferred the Brazil side just because it was great to be there without so many tour buses.