If you are leaving from IGU, definitely stay on the Brazilian side as crossing is a lottery and the last thing you want is to stress out about your departing flight. I usually stay at Carima Hotel, on the Brazilian side, just 2 miles from IGU: You get to enjoy the hotel until the very last moment.
If it were me, I'd overnight at least my last night on the side where my flight departs. If you're leaving from the Brazilian airport (IGU), better to stay on the Brazilian side. That way, you have only a quick taxi ride to the airport. It's less than a half-hour from downtown the Brazilian city of Foz do Iguaçu. From the national park and the Brazilian falls, as well as from many of the hotels on the highway between the city and the falls, the cab ride will be half that.
If you overnight on the Brazilian side at a hotel not far from the airport, you could leave your bags in the hotel while paying a quick visit to the falls. Then, on the way to the airport, have your taxi swing by the hotel to retrieve the luggage, which you're confident is safe in the hotel check room.
If you overnighted in Argentina, not only would you have red tape at the border, but your taxi ride is longer and you might run into a crowd waiting in the queue to cross, say a bus.
No a problem in June, for you, but if anyone were traveling between October and February, Brazil turns its clocks ahead for Daylight Saving Time but Argentina does not. If one were careless, you might forget that fact, only to find that the Brazilian flight leaves one hour earlier, Argentine Time, than you thought.
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