Genuinely curious! From my perspective the postdocs have even less freedom than I do (I work in a national lab, where although I'm a PhD student my experience sadly is more like an employee). I know research fellowships are different, but seeing as most people go PhD -> Postdoc, this to me does not seem like a step forward.
EDIT: I am from the UK, but some of the answers below are about the US. Does seem rather different over there!
They are assigned tasks by our boss, and they have to do them. I remember this postdoc, smart guy, who had an interesting idea but the boss said "sounds interesting but that's not your work" (something he has said to me). Now I can (and have) bent the rules to do more of my own thing. I don't have to come in 9-5 in the same way the postdocs do. So for less research and work freedom they are paid a bit more than me. But after tax, it's not some huge difference?
So why don't we see more people do PhD --> PhD, instead of always PhD --> Postdoc? Seems like the life is better!