I drove the Compass Latitude and the 19 Cherokee Trailhawk on test drives. The size of the Cherokee make them good comps.
The Trailhawk was the 2.0 Turbo, and the Compass was a 2.4 naturally aspirated.
The Compass ride was smoother both on and off road. The pickup was less, but not demonstrably so - and very surprising as I expected the Trailhawk to kill the Compass.
What I would expect overall is a stiffer ride depending on the kind of highways you are driving on, but more capability in less ideal circumstances.