The principal differences you will note are:
1. Not waiting in line at the rental place
2. Feeling all smug and vastly superior to everyone stuck in the rental line or standing in the lift line on obvious rental boards
3. Being absolutely convinced (whether or not it is true) that your new skis are such an unbelievable improvement over the rentals that you're skiing at least two or three times better than you ever skied before.
4. Suddenly feeling very, very, very nervous about leaving your skis when you go in to take a pee, eat lunch, etc., wondering if you need to either lug around a lock or use the ski valet
5. Realizing that, bad as standing in the rental line is, now you've got to lug them to and from the car, or worse, pay through the nose to put them on the plane.
6. Taking them out for the first time after a summer in storage and realizing that you need to take them to the ski shop for a tuneup because of the suggestion of corrosion on the edges, nasty little nicks and scrapes you didn't notice when you stored them away in the Spring, and the suspicion that somebody who knows what they're doing needs to check the bindings before you do any sking on them.