When EWR-GIG first started it flew all night there and then back to EWR during the next day. People complained because they didn't want to take a daylight flight to the states. So CO changed it to an all nighter like the one south bound. SO customer preference plays a big part. The daylight flight north bound from Brazil was not successful. Most flights to Europe fly all night and the plane turns around and flies back that morning or early afternoon. The crew rests for 24 hours and flies the flight back the FOLLOWING day. That schedule makes sense because with the time change a west bound transatlantic flight lands only a couple hours after it departs Europe. With South America there aren't so many hours in time change. Therefore if the flight turned around and returned to the states that day you'd land many hours after you take off unlike flights westbound from Europe back to the states. So you'd be consuming the entire daytime on a plane. Maybe customers in that market don't want that. I mean during that day you could be conducting business. That's what CO's experience was.
Even though I'm not sure about this one, I don't know if the same crew would actually fly the plane back to the states that very same night of the morning they arrive. Let's think about it. That mean being up all night working two nights in a row, 9 hours a night. That seems a little extreme. After a 9 hour flight, if you only have 12 hours rest, by the time you passed customs and got to the hotel, you'd better sleep WELL for exactly 8 hours because at the end if that time you're going to need to get ready for the flight that night, without even having any time for eating. If you travel a lot and cross time zones you know that sleeping well in strange places all the time isn't easy. As I said I might be wrong, but I'd be shocked if the same crew flew back that night. I think only 12 hours rest for a nine hour flight is a little short. Besides if the flight were late arriving , the returning flight later that night would have to be delayed do the crew could get their required rest. So there's no flexibility in that respect.
Crew scheduling probably isn't the reason for using two aircraft to south american cities. It's probably more consumer prefenence. As I said flights back to the states from Europe use crews that have had 24 hours rest in Europe. The plane doesn't just sit at the airport in Europe waiting for the crew to finish resting. The plane flies back using a fresh crew. Flying all night the night before then again that next night, you probably won't be too rested. I expect the crews on these south american flights rest 36 hours and fly back the following night.
I hope this helps.