Although to me, this is an odd thing to hear. It is well spoken English and maybe implies the person could be overweight, or a nuisance somehow, and they feel like and are reminded of the fact that they’re a burden whenever they go onto an airplane. The second doesn’t sound natural to me, but the meaning here is more direct, and more of a statement. “I feel like a burden when I go on planes” Where the first sentence implies of all the things they do, the feel the most like a burden when they enter the airplane.