Alright, the sort of original detective Batman is not as smart, but at the same time current BAtman is super smart to a crazy degree. Same degree as Tony or Reed to be honest. I dont think he should be but he is in the same intelligence ballpark, but different specialty.

In pure intelligence as written I think he has her beat, but she is a better strategist and tactican. She is even a better fighter overall than he is, but fact of the matter is that Batman is the prep master in DC, bar none. I think in actual battlefied on the spot intellect WW has him beat soundly but if you sit the JLA around a table and talk strategy its going to be Batman doing alot of the talking with WW chiming in and being the only one to really question or add anything. He finds the weaknesses and its the only way he is able to fight some guys that he does, does that mean he is smarter than her, no but when you have so many powers other abilities are more masked even if super. Batman and streets on the other hand that have a power you see it all the time and are nearly always in awe of it. IMO.