I don't think you'd notice any difference in stability. I have driven my 2500 towing a 14,000# 5er, and been a passenger in my buddy's 2014 3500 SRW Cummins towing the same 14,000# RV 5 min later. The difference in chassis and suspension was discernible, but not unless you were in them back to back, and even then it wasn't huge.
There is more of a difference in powertrain performance between the gas and diesel, but either would tow the two RVs you mention pretty easily.
I was am in the same situation as you (tow only for holidays in the summer), and I chose the Hemi and haven't regretted it one minute.
