OBBs intersection improvement for AABBs-OBBs
Broad Phase collision detection

It looks like you are using this for what is called broad phase collision detection. This is the step in collision detection that is used to determine candidate pairs for the narrow phase that does the actual collision detection (Quick Summary)

As this is a bounding box text (especially if you are involving AABB) it looks like you're just trying to see whether to go through the actual intersection routing of the two shapes or not. If you can just stick with AABB in general, the math gets a lot easier and therefore faster. Also moving forward you can employ AABB-trees (they are space partinioning trees) to find all intersection candidates for one object with a tree query rather than a pairwise check.