I'm based in MVD and have flown TAM, Taca, LAN, AA, Copa, and who knows how many others. Going from Uruguay/Argentina to California. Right now i choose AA... LAN is nicer, the long haul planes they use for south america are nicer, the crews nicer, etc... But AA gives better miles, full miles on discount fares vs %33 on LAN.
Some days of the week LAN has great connection times, just an hour layover, but unless you're careful, some days they'll give you a 8 hour layover in Santiago.
Taca and Copa are not great airlines... avoid.