I've recently done some flights to/from S.A. on both LAN and AA over the past couple months.

Seating: I would give to LAN (unless upgrading to F on AA). The seat goes fully flat (no angle), and you feel like you have more space in front of you when in seat/lounge mode. AA has more storage areas though.

Catering: I give LAN a slight edge. Items seem a bit more put together and upscale. Presentation is better. Wines are a bit better too.

Service: I was expecting that LAN would have great service, like QF, QX, or BA. The reality was, on multiple flights, that the FA's would completely disappear after the meal services. During service they were good, but they rarely were back checking on people. This of course happens on AA also, but overall the AA FA's were much better on these recent flights. I wouldn't say LAN's service was surly, it just lacked some friendliness.

IFE: LAN has nicer, larger screens. Better selection than AA.