Are either SP or Rio worth a day's visit vs. no stop at all or vs. a longer stay?

I assume you know that, depending on where you're from, you may need a visa for Brazil. I'd get it ahead of time rather than trying to do it in Buenos Aires, etc. I'm not sure if there are tours form the Argentine side of the falls to the Brazilian side for which you don't need a visa. Definitely need one to fly to SP or Rio. I'm not familiar with SP, except for the international airport out in the city of Guarulhos, though an American friend who lives in Brazil actually prfers it to Rio (shopping and museums and restaurants). Rio would be a good stop for at least a full day of touring. I'd stay in Ipanema or Copacabana, in a hotel on the main beach road. The main airport there (GIG) is nothing great, and gets some desrved criticisms on this site, but I don't think GRU is so much better that it would affect my decision as to which city to visit.

Note that Brazil is, by and large, more expensive than Argentina. Brazilian prices are often a rude surprise to foreign tourists.