11K lbs towing is fine with either gas engine truck. Fuel mileage will be worse, your engine will be in higher RPM range towing and on certain long mountain climbs you might not be able to maintain your speed to the top... but if you are okay with those parameters you should be perfectly fine with a gas engine.
Sorry to hear about your Ford, I would agree that sounds like a lemon truck rather than known or widespread issues. Word of caution, research the heck out of either truck before you drop the money. My friend bought a 6.4 Hemi with the old 6 speed and only the 3.73 gears. He was not happy with it towing because it had a odd gear spacing and would drop from 4th straight into 2nd when pulling mountains in central PA, completely skipping 3rd gear. He was well within the weights, but it didn't like pulling up hills with that rear end and trans ratio. I'm sure Ram has fixed that with the new 8 speed, but read reviews just to be safe and make sure you get the right rear axle ratio.
