Either will tow a trailer up to the limits of their rating without much trouble.
Quite often a Class C will have a hitch rating of 3500 lbs. This rating MAY be increased by strengthening the frame extensions and the hitch, IF you can find a shop that does such work on a regular basis for trucks. There are such shops out there. The limits based on engine power and/or transmission life are much more difficult to change, but it can be done.
Class A motorhomes typically (but not always) have a hitch capacity of 5000 lbs. This, too, can be changed by reinforcing where needed.
Many Diesel Pusher motorhomes have a hitch capacity of 10,000 lbs.
It is very likely you will have to install a brake controller in the motorhome. Not many people tow trailers with them, so a brake controller isn't often installed. Of course, you could get a trailer with surge brakes which would take care of the problem.
