The E-350 is a heavier duty chassis than the Promaster. Depending on the specific variant chosen, the E-350 with dual rear wheels (which is what would be used for a motorhome) has a GVWR of 11,500 or 12,500 pounds. The Promaster 3500 has a GVWR of 9350 pounds and is only available with single rear wheels. Many of the promaster-derived motorhomes have pretty severe weight carrying limitations--you can be over the rated weight in some cases just from a couple of people and a tank of water, without taking any other cargo or belongings.
The E-350 also has a much larger fuel tank, about twice the size. (This is somewhat offset by it's having a thirsty engine.)
The Promaster is the nicer vehicle to drive, assuming both are set up with reasonable balance and so forth. It would also be more maneuverable (tighter turning radius, etc).
I'd generally prefer the Ford chassis for a motorhome, primarily because too many of the ProMaster-based motorhomes are just a little too much for the chassis.