We used to tow a 2100 pound Toyota MR2 Spyder. We then switched to a 4100 pound Jeep Liberty. The 2000 pound difference was very noticeable. That does not mean it's a problem concerning power. The concern for me was braking so I got a good tow brake kit and all is well.
Don't skimp on a tow brake. There are some great kits available and some that are marginal. Ours in our Liberty is a permanent installation which maintains vacuum in the power brake booster so the cable driven braking solenoid is much more effective. Also with a permanent installation, there is nothing to see and nothing to fuss with. The only matter at hand is that it is difficult to remove and install in a replacement tow vehicle.
If you end up towing the 5500 pound vehicle, you will be over the rating of the hitch which is 5000 pounds for just about every class C. It used to worse. Most older class C motor homes made prior to 2005 were equipped with a 3500 pound hitch. I have not heard of a class C with a hitch rated higher than 5000 pounds. You will want to look into that before making a final decision.