We have a Corolla. The "CE" was base model in 2006 and is what we have. The next two up were "S" and "LE." CE has the same wheels as S and LE, but standard with one tire size smaller. We upgraded to the larger tires (and the spare to full size which fits the well) and it made the car even more pleasant.
The Vibe is a little more than a Corolla Hatchback. I know it uses a different Roadmaster Base Plate, but I don't know why. I think Vibe has larger wheels and tires.
We currently tow my Nissan Frontier since we go to beaches and forests and like to carry dirtier stuff that I'd rather not have in a sedan or SUV. But the weight difference is noticeable in the towing.