Almost 3 years ago, I replaced a Mazda Miata (MX-5) with a Model S. Wow, the Model S was huge by comparison. ;-) It still feels big to me, but I've mostly adapted.
Parking was a pain at first, but the auto-tilt mirrors help
a lot with that.
The car is a lot wider, which is just something you have to get used to. Pay more attention to where you are in the lane; you have less wiggle room.
Really, I feel like turning radius is the biggest thing that there's no way to "adapt" for - I have to take turns slower and wider. I mean even slow ones in parking lots or parking garages, to say nothing of, say, a left turn onto a divided road. Be very careful until you get more used to having such a big car. ;-) Early on (and maybe not that long ago, blush), I took turns too sharply and grazed or went over curbs. I'm mostly over that, though, honest! LOL.
Also, bottoming out when I would never do so in the Miata. I learned to take certain steeper things at a slight angle or a
lot more slowly. Although, again, the car has a feature that helps -if you got the air suspension, raising the car via that! This has helped for even a situation where going as slow as molasses didn't help - I love the air suspension.
- - - Updated - - -
How has your driving experience been with Model S if you went from a compact car to Model S? What have you had to do differently with Model S due to its larger size in normal driving, changing lanes, parking, etc.?
P.S. you didn't mention what your old car was.

What was it???