It sort of like comparing a Chain saw to a hand saw. A belt sander is typically for rougher work. They can take off a lot of material fast and that means you can ruin what your working on much faster. :-)

A properly set up hand plane will be taking only a very thin sliver off with each pass. So it's going to take longer but you sneak up on the finished surface instead of roar past it.

So the answer really depends on what you want to do with it. Personally I would take a hand plane over a belt sander any day. I have both and rarely use the belt sander but it does have it's place. I have several different hand planes and I use them all the time. If you don't have a plane I would say start with a block plane, it is the most useful and by far my most used plane.

Of course, keep in mind you need to be able to sharpen a plane. And to work really well sharp means you can shave hair with it. Scary sharp is a good way to start and it's cheap.