Latin America is huge.
Are you really going to be traveling all over South America? or specific cities/countries?
Also, are you traveling business class? or economy?
For example, if you are doing a lot of (northern) South America (Peru, Colombia, Ecuador) then you will most likely be stuck with recliners on AA(domestic F), i.e. no lie-flats. But if you are flying economy, then that does not matter.
If it is really all over South America (Ecuador, Colombia, Brazil, Chile, Peru, etc) then I would not try to stick with just one airline but two (probably UA and AA from ABQ).