Welcome to the forum.
The GCWR and GVWR ratings are most important. The Allison 2500MH in the 340 limits the GCWR to 33,000 lbs. (forget the hitch rating)
You need to first figure how much you will load the RV (with occupants), see if that is within the GVWR and then subtract that from the GCWR, which will give you what you can tow. You can get your fully loaded weight by having your motorhome weighed (fully loaded) after purchase, but that is not what you should do. See.............
RV and Vehicle Weight Definitions
With the UVW and CCC ratings, you can do some calculations. Unfortunately, these ratings are not always supplied.
The yellow sticker on the motorhome's front door has information not in the brochures. You should get that info.; it will help you decide. Forget the Hp difference between the 340 and 360, the load carry capability is most important.