I have traveled from Dallas to Tegucigalpa on both air options, American through Miami and Continental though Houston.  I am sure your choice will depend largely on where you live.  If you are in a situation to select one or the other, I would definitely recommend Continental.  I have learned to stay away from Miami's crowded, crazy, and hectic international terminal.   With only one flight a day arriving in Tegucigalpa via American and Continental, selecting the correct air carrier is extremely important in order to make your connections and to have a pleasurable day of travel.  If you have not been through Houston's George Bush Intercontinental Airport, you need to.  After taking the Miami route twice before, how pleased I was by selecting Houston on my last visit to Tegucigalpa.  Houston's new international terminal is beautiful and has plenty of room to maneuver with no long lines or crowds that is often found in Miami.  This route, which is much shorter for me out of Dallas, will also get you into Tegucigalpa one hour before American's flight.  Once arriving in Tegucigalpa, you will be pleased with the new "modern" airport that is still under construction.  (It beats the one-room shack that used to serve as their airport.)