(too late to edit my previous post)
Copa's planes beat AA hands down, both in age of the aircraft and cleanliness. The Panama City airport may also be one of the nicest airports I have ever flown through. Modern, spotlessly clean, lots of duty free shopping choices - only drawback to me was a limited choice of places to eat in their airport.
Also, you have the option of flying through Panama as in-transit status, which means no immigration or Customs for Panama, and (knock on wood) the luggage always has made it to the next Copa flight with no problems, even with connection times of less than 1 hour. (try doing that in Miami !)
You can normally also get the same ticket prices if you choose to layover in Panama for a day or two of shopping or sightseeing, if you use the Multi-City approach for flight dates.
Just for schitts and giggles, I also tried MIA - Panama - Santiago Chile and the price was US$1957 for 2 people including taxes and fees on Copa for the same dates.