Well aren't I the expert of the day! My driveway has both a Corolla and a Fit!
I have a hitch on my Corolla and I use it to haul 3 bikes at a time. It is our family bike destination machine. I also pull a 4x8 trailer behind it very easily, so it is also our "truck". I think the hitch cost $200 and the wiring harness kit cost $40 some years ago. My Corolla is an old model with an antiquated 4-speed automatic that only gets around 30 mpg. I lust for the hybrid but so far I've had zero issues in 8.5 years so no bitchin' here.
Our Fit gets about 32 mpg (manual transmission) and is much more fun to drive, whether playing the sports car game or the hypermiling game. It does have a decent amount of road noise though, and the smaller tire circumference means it has a bumpier ride at high speeds. As
@Just Joe guesses, it is louder on the interstate and buzzes along at 3500 rpm. This is what it's designed to do; I've found Honda motorcycles are also geared a bit low and so it brings back happy motorcycling memories. I never got around to spraying undercoating on the Fit, which would quiet the ride a lot, judging by its effect on the Corolla.
More to your point, if I want to carry my 29er mountain bike in the Fit, the front wheel generally has to be removed AND it has to go in diagonally. This is the same amount of trouble as plugging the hitch rack onto the back of the Corolla, and it consumes most of the storage space in the car. I also hate to pull off the front wheel because of the risk of bending the brake rotor as things clang around in the back. When we took the Fit camping, for example, and needed the interior storage, I used my cheap strap-on rack against the trunk. But if you're going to use a strap-on rack, it could as well be any vehicle.
TL;DR: Put a hitch on the Corolla and buy a hitch-mounted bike rack.