Batman uses techniques from 100+ disciplines. BUT, he does have a style.
It's hard, fast and stealthy, based around him tanking as few hits as possible while causing the greatest amount of damage. Its about controlling the situation and adapting faster than the other guy to things that change - i.e. just the sort of style you'd expect from Bruce's personality. It's very different from Supes (tank and punch until it dies), WW (rush in and try to pwn it hard) and Flash (avoid, avoid, avoid, taunt, big fast hit). Its even different from NW, who tends to be more acrobatic and flashy.
(This is why I loved DC animation, because you can show this sort of characterization easily - even JL and JLU had stylistic differences between the founders).
1. Supes costume is better for a cover, its brighter and very iconic, more so than Bats.
2. Supes is always the leader/figurehead in teams (i.e. situations were we would need a pick with both of them together). He is the icon, after all. Leaders go in front.
3. Personality wise, Bats is far more likely to avoid a dynamic entry/flashing pose/etc, being the (k)night and all that. I like covers/poses to reflect personality, so I almost prefer Bats being further back, shaded and generally looking scary.
This does seem to be changing at the moment. We have more Bat books right now, and there is no hugely successful new Supes trilogy.
Seems Blue has the power (two Kryptonians, Apocalypse Thor) and Silver has the smarts (Doom + Capt gives us awesome strategy and tactics, respectively, Steel is no slouch). Team Green is the most adaptive - we have two GLs, AMAZO and the best shapeshifter in DC. I pick Green winning, because I think that adaptability is gonna give them an edge with such a huge brawl.
Other than Bats, Storm and Black Adam, team Black doesn't seem to have a lot, I think they'd just be overwhelmed and lose quickly.