I've noticed it helps my general riding skills A LOT to ride different horses. While the basics of riding may be similar, each individual horse seems to have different things that make her or him tick. Some are more sensitive to cues while some need a bit more motivation. Some have a smooth gait while some have a rocky one, etc etc.
Instead of being used to the same thing day in and day out, riding more than one horse makes you a better rider since you have more experience dealing with different things.
For example on one lesson horse I had no problem sitting the trot. She made it all too easy! But my current lesson horse has a trot that's quite jarring. Riding him has taught me how to better sit the trot. With out switching horses I would be "behind" in that area since I was so used to a smooth trot.