I've flown both in first on the JFK-SCL and MIA-SCL routes over the last six months. Without a doubt, go with Lan Chile. There's no 777 service to Santiago on American, for now, so it's all 763s.

Since there are only 5 seats in LA first class, the service is superb. The food is delicious, and includes caviar. The inflight entertainment depends on whether the 763 has been updated with the new interactive system. Otherwise, it's a choice of several films and audio selections.

Seats recline fully and are comfortable.

Nice amenity kits, great first class lounge in SCL.

Enjoy the trip.