The diesel has a different acceleration profile, it sounds different as you would expect, it has different maintenance requirements such as DEF and oil, if you are going to be where it gets bitterly cold you'll want the engine block heater.
Diesel fuel is oilier than gasoline and smells different. The oiler part is why diesel pumps can appear to be dirtier than gas pumps as it simply doesn't evaporate in the same way as gasoline. It also will stick on your hands in the same way where gas would evap and seem to be 'less dirty'. I have a little pack of hand wipes in the door pocket in case I get fuel on my hands. It's not a big deal to me. I never smell diesel from the Escalade unless I am refilling so no, it doesn't smell like a big diesel truck does when sitting in the garage.
The diesel is also much more efficient in fuel economy terms. I just did a round trip from Colorado Springs to Palm Springs, about 1100 miles each way. I averaged 25.3 out, and 26.2 back, with two adults, two dogs and a loaded up cargo area. I tend to drive 10-15MPH over speed limits, so between 75-90MPH speeds up and over the mountains.
The diesel can tow about the same weight (I don't remember exacts) and often does so easier as it has more torque lower in the power band. It will also maintain superior fuel economy when towing, and in my experience the gap widens.
Our Escalade is primarily for road tripping or extended trips between properties. The only thing that would make me choose the gas version would be because the diesel wasn't offered anymore.