We've both rented and lugged, and we prefer lugging.
Our experience renting from Avis was pretty bad. For one thing, they didn't have the carseat for us when we arrived to pick up the car, and we had to sit around waiting for it for 10 to 15 minutes.
The carseat itself stank of Febreeze (very chemical-ly, and the guy said it was Febreezed) and was really basic — not at all padded or supported, and even though it said it was for babies five pounds and up, our 3-month-old slumped so badly in it that I had to stuff a bunch of rolled-up blankets in it. Plus, there was no way to adjust the angle of the seat, and it ended up being way too upright for a baby who can't sit up on his own. We were able to tilt it back a little (thanks to the thick December issue of Vogue and DH's computer books!), but I sat in back with him the entire trip to make sure nothing slipped. It definitely wasn't comfortable for him.
The next time we traveled, we brought the Snugride, and it worked much better. The fact that it fit in our stroller made it easier to get around in the airport. Airline employees went out of their way to help us, and it was nice to have the carseat in his airplane seat, too. He slept very well in it!
Our next trip will involve us lugging the Britax convertible, not the Snugride, so we won't be able to snap it in the stroller, but I still think it will be good to have it. (It's the Roundabout, the smallest model, so hopefully it fits in his seat.) I hear it's easier if you just pull the straps out all the way, which then allows you to throw it over your shoulder. We'll see if that works for us. Or maybe we'll get one of those wheeled carseat-carrier contraptions mentioned earlier.