Character wise they are very different with opposing philosophy's of light and shade, so a lot of the material evolves around that. However they both respect and value each others strengths. Think along the lines of a couple of brothers of opposite character who fundamentally love and respect each other but fight and bicker on the surface. Only to come together and kick the crap out of some knob head who besmirches the family name.
Tactically; obviously superman has the real superpowers because of that he can tend to tackle things head on sometimes without due thought. Batmans super powers are essentially his money and his sense of devotion and self discipline. He tends to be more tactical thinking things through to be one step ahead of the game. Again opposing philosophies which in the correct situation can compliment each other.
