Both of those statements convey the same meaning but when you say "Some dreams are different from others," it implies "other ones". Personally if I had to choose for you, based on brevity alone, I would choose "some dreams are different from others". PS- you can also say "Some dreams are different from each other."

I agree with Ryuichi. Generally speaking in English, we look for ways to simplify and make things shorter. Therefore, the first option would be the one I would choose if I had to pick one.