I am about to start commuting from ORD to GIG, on my own dime..
AA has tickets from about $1200 on a 767-300.
UA has tickets from about $1200 on a 777.
JJ has tickes just above $1200 also on a 777.

JJ also can be used on domestic flights but is G3 would be considered a better airline?

Any suggestion and input? Thanks..

For me, JJ and G3 are absolutely the same as far as the flight is concerned -- very cramped and little or no service. But G3 is officially a budget airline, whereas JJ is supposed to be full service. Between these two, I would choose by schedule, price, or where you want to earn miles. There is also OC, formerly known as Ocean Air, now Avianca. It offers MUCH more space between the rows (pitch, as they say) as well as a snack and soft drinks. It is also usually much cheaper than JJ or G3 if you are buying the ticket in Brasil. This is not to mention local airlines such as TRIP or WebJet, the latter now owned by Gol. I would put WebJet in the same basket as Gol and TAM; I have heard better things about TRIP, but have never flown it myself.

If you're going to be commuting regularly, you will soon get status on any airline you stick with. I think you should look into which airline is more likely to clear upgrades on this route.

5 trips @ 10k+ bis gets you mid tier on aa or ua....i echo the idea of concentrating on 1 carrier....

If you are interested about doing this on UA, I've flown this route twice.

The best connection is ORD-GRU-GIG and back. On the trip to GIG (UA845 connecting to UA861), It is a 40 minute connection at GRU.

The connection at GRU is virtually guaranteed. They held UA861 in GRU for us on one trip for about an hour. I talked about it with one of the cabin crew and they indicated they typically wait for UA845.

Your travel time will be about 12 hours to GIG and 13 hours on the return.

On Mileage Plus, you would be Silver after the third trip and would get free EconomyPlus (at check-in), if it is available. From my experience, E+ was pretty empty flying midweek.

After the fifth trip, you would be Gold and be able to select an E+ seat at time of purchase for free.

I would recommend travelling with UA. It's really the best option out of CHI.

You can also speed up AA status by doing some cheaper MRs on the ORD Double miles promo.

AA you would need to connect in either MIA, JFK, or DFW but there would be no tag flight out of GRU. The AA 767-300 has no inseat entertainment system if that is important to you.

On AA you could do a Platinum challenge and, depending on the fare, earn Platinum status with a single round trip.