We reside in Brazil. 3+ hours probably sufficient, but I'd probably go with the earlier flight, since the TAM fight could be late, and/or the airport crowded during the holiday season. And if you miss your BA fight you could have problems (no flight until the next day, I think, and that assumes there's space). I don't think you'll have to collect your bags (check with TAM in advance). We haven't had to when we've connected domestic-to-international at GRU, but we had purchased our entire trip as a through ticket. The fact that you will apparently have two separately-purchased tix could make a difference. Although our bags were checked through, we still had to leave the secure area and stand in line at the counter of the airline operating our onward flight to the U.S. (did this on different trips, with both United and Continental), along with those just starting their trips at GRU in order to get our boarding passes. Then went through security, and passport control, to our gate. Counters of foreign carriers sometimes open only 3-4 hours before their flights leave. There is a better variety of eateries outside of security.

International-to-international is an entirely different system. Don't see how anyone could guess whether someone would make that with a short connection. Will both flights be on time? Will airport personnel be efficient in the transit area? The airline(s) involved apparently felt it was sufficient time (though if someone misses their flight they may have to stay overnight, and if they don't have a visa they can't leave the transit area), assuming both flights were purchased as a through-ticket. Besides, if someone already bought their tickets, it's a moot point.

Overall, I'd rate TAM and Gol about equal. TAM is part of the Star Alliance, and Gol is a code share partner with American Airlines (but not part of the OneWorld alliance), if that makes any difference.