The Rubicon comes from the factory with taller springs and shocks. It also has higher fenders than the Sport. However, you can run 35's on your stock Sport on the pavement with no rubbing. I would expect you to have significant rubbing off road.
There are 2 types of tire rubbing to look out for. Rubbing against the fender from up and down movement. Rubbing against the Jeep's undercarriage when doing a full turn.
The Rubicons come with longer axles so wheels will fit them differently than the Sport. Pay attention to the backspacing/offset of the wheels to avoid rubbing when doing a full turn. I would speak to the company selling the lift to find out what backspacing/offset will work before and after the lift.
The video shows a JLU but the principles are the same for a JL
