I am unaware of any direct flights (haven't checked though): Copa will fly via Panama City, Avianca via either San Salvador or Bogota, American via Miami, and Latam via Lima.
If you are purchasing economy tickets, my personal preference in Y would be Avianca or Copa. I feel they are a bit better than AA, but haven't flown Y on AA on such a flight for a while now. I also like to avoid Lima like the plague, hence not recommending Latam.
If you want business, the costs are not that bad for purchased tickets on any of them, but if you are "into" lifemiles, Copa and Avianca have great availability for cost-effective J awards bookings. Regarding business flights, most options will be on narrow-body (single aisle) aircraft, mainly 737's or A320's, so if going in J do not expect anything more than effectively "domestic" business hard products. If you search, you may get an A330 or 787 with Avianca as far as Bogota, or a 767 with Latam to Lima, but this takes careful searching.