I have a 2015 Grand Cherokee, V6, gas. I have towed our TT from the East Coast out to Yellowstone, down through and into the mountains of Colorado and into New Mexico and it towed like a dream. I have also towed with it down to the Keys and back plus a lot of regional trips.
I tow in sport mode. It never hunts for gears. I watch the oil and transmission temps and they always seem to stay in what I consider a safe range.
My trailer has dual axles with a little bit of space between the axles. I have a WD hitch that uses friction bars. The TT sits nice and level. I don't experience any porpoising and the TT tracks nicely with the TV.
Your experience may be different depending on the TT you get and your hitch set up.