I have flown both very often and am TAM Vermelho (their highest status). JJ has quite nice but small lounges in GRU and GIG, and is easier in all respects to deal with than is G3, JJ website is not very good but consistently works when you use Brazilian domestic credit cards. G3 has presented all the problems for me that Winged Explorer discussed, plus an absolute inability to get a refund or adjustment when they cancel flights. I would continue to use JJ in preference even without the miles on OW were I in your position. Soon JJ's new alliance will give you another option.

A couple general comments on flying in Brazil. Inflight service is better on any carrier in Brazil than on any carrier in the US, IMHO. I've done a lot of both. Ground services are not too consistent and delay information is spotty at best. Web services are poor and call centers are also, although every single person is unfailingly polite and courteous. If you keep very polite and use social niceties (eg good afternoon, miss/sir, I'm sorry I have no Portuguese but...) you'll have fairly good success, including using elite lines when flashing unaffiliated cards. If you are irritated you'll have bad results every time. Come to think of it these may be good principles anywhere.