Batman is the brains of the league.
Superman is smarter but was raised on a farm in Kansas and has had little exposure to thinking on a tacticle and strategic level.
Wonder Woman is a warrior and thinks like one first without reguard for the consequences.
Martian Manhunter is an alien and has a non human thought process.
Flash thinks faster but is at heart a scientist and examines everything through that lens.
Green Lantern is a fighter jock who takes risks.
Batman is the only one who has trained himself to think like a leader. An in depth planner and multi level thinker is needed for the league as much as power and speed.