I've flown Delta out of Atlanta to Belize many times. (Flights from other cities connect to Delta service from ATL.) They started service several years ago, with daily two-class service on 737s. Then they reduced service to a regional jet on weekdays and two-class 737 on Saturdays only. Then they cut back to less than daily on a seasonal basis. I'm not sure what their current service is. I used to be a big Delta fan, but with all the changes in the airline business and with Delta management they're now just another U.S. airline.
I will say this: Last January I was flying out of Atlanta to BZE, and there was a big (for Atlanta) snow storm. Delta canceled just about all its domestic flights, and the airport was a zoo. But Delta kept their international flights operating (that's where they make their money), and despite the snow I got out of ATL on time and actually got to BZE ahead of schedule.
3 of 5 trips to BZE have been on DL. The last two were on Continental due to more favorable schedules, but with that said I just booked another trip this weekend for September on DL. Truth be told tought it was because we had enough Frequent Flyer miles so its hard to argue with free.
I saw over the weekend that AA had some killer fares to BZE, but the returns spanned 22+ hours, which is too painful for me.
I always try to fly Delta as they have direct flights from ATL to BZE (< 3 hrs) and I can usually use Freq Flyer points (which is huge). Not sure why, but my experience has been that their customer service has improved over the last year. Another plus is that Delta allows 2 checked bags at 50 lbs limit and a 40 lb carry on.
My only experience with American is I had to go through MIA (can you say nightmare?) and they lost my dog -how does one "lose" a 70lb pointer? I did find him the next day in BZE airport... not my best day.
Continental is ok, but they charge extra for baggage and of course nothing direct from ATL.
Just got back Sun. on Delta, I always fly Delta, no problems at all, had to pay new 3 dollar tax leaving, no baggage fees on Inter. flites. Plane was about halve full, We went Cinn.Atl. Belize. My bag was 1 lb.(51) over so I had to take out a pair of pants, I had 4 litres of Rum & 7 bottles of hot sauce in it to survive till my next trip in Oct.