Dream is kind, caring, extremely pacifistic, and childish. Dream doesn't exactly understand why Nightmare dislikes him. 

Both Dream and Nightmare are 531 years old and twins though they no longer look alike at all.

Nightmare was one of the kindest beings in the multiverse at the time. He cared about everyone and loved all. He had a deep love for flowers (mostly roses) and animals. He had great charity, which could have been part of his downfall, because of how much he gave to others.