Do old fish behave differently than middle-aged fish?

Not only can they behave differently, they can look different too. Some fish will move more slowly, some fish may appear to be "resting" more often. Some fish colors become more vivid with age, some fade with age. Some loose their markings with age, and others develop other markings as they age.

So it's not really easy to answer that question when talking about all fish. When talking about a specific fish it's easier to answer.