We travel with ours & check them with the luggage. We have travel bags for them that have wheels & backpack straps. They check for free & you can cram all the diapers, wipes, and anything else you want for that matter in the bag & they don't charge you- as long as there's a carseat somewhere in there. So it ends up saving us a little money since it cuts back on the number of checked bags we need. We've never had ours damaged in any way during travel & we're coming up on our 11th & 12th flights with carseats. If you're worried about them getting damaged, then I'd buy a really lightweight, cheap carseats & check them- they're near indestructible. Dealing with carseat throughout the airport, security, and on & off the planes is a deal breaker for me. Way too much work, plus they take up a lot of room in the row itself. My kids like to move around some & play more freely where if they were in their carseats, there's not much leeway or space.
One time we rented them through the car rental agency. Not only are they dirty & expensive but you still have to install them yourself & now you're dealing with an unfamiliar carseat, with no directions. If I have to install a carseat, I'd much rather one I know well.