I brought a carseat on a plane for one trip. I had one of those carts that attach to the seat to roll it around and I though it was ingenious. Actually it was a huge pain in the rear. Firstly, my carseat, a Britax, was too wide to roll down the aisle so the cart was useless on the plane, worse than useless because for some reason the one I used attached to the carseat with long screws which took forever to put in and take off. I was travelling with my kids on my own so a stewardess had to carry the seat down the aisle for me over her head and then i spent 10 minutes propping it up and unscrewing the cart. Installing it was cumbersome and once it was installed it lifted my child up and forward, putting him in the perfect position to kick the back of the seat in front of him. I ended up taking him out of the seat anyway because there was no way, short of removing his legs, to prevent him from driving the poor passenger in front of him completely bonkers. At the end of the flight i nearly strained my hand trying to unbuckle it (helpful tip, you need to turn the buckle side of the belt upside down when you install it or you'll never get it unfastened) and then had to do the entire process of getting it in there in reverse. If you're not renting a car you then have to muscle the darn thing out of the airport and onto a bus and then store it in your hotel room.
In conclusion I recommend the CARES harness. It's very easy to install and provides a chest strap and shoulder harness keeping your child safely secured at the back of their seat and saving your back, arms, and sanity. I want to add that one of the previous posters mentioned that the cares harness could be dangerous if the adult holding the child is thrown against them. I think she might be thinking of a baby carrier or sling which could be dangerous during an accident for exactly the reason described. The CARES harness is not for lap children and can only be used by a child in their own seat.
Good luck, have fun!