I tried to take mine with us to Hawaii and was so thankful they made me gate-check it. (We hadn't purchased the airline seat for my daughter, then 22 months, and even though the airline seat between me and my mother was empty they made me gate-check the car seat.) It is big and bulky and trying to wrangle it up and over the seats AND not lose the child, ugh! As it was, it was awful lugging the thing through the airport (and we had the thing that attaches so it could be wheeled). I do not recommend the wheels if you plan on taking it on the plane, it was a hassle to attach, detach, reattach, every time we boarded/disembarked/transferred. The wheels have to come off to put it in the seat, and you need room to maneuver, which means doing it at the gate. You don't want to have to do that if you're running the slightest bit late.
She was also more comfortable in the airline seat, could lay down with her head on my lap to sleep, and my mother and I (on either side of her) had more elbow room. The seat would've taken up A LOT of wiggle room and we would have been much more cramped. Not fun on a 14 hour flight.