Typically intersection checks outnumber updates, so it's better to optimize the former. Also, that only works if the object's pivot is at the center of the bounding box or you're accumulating movements without an explicit position.

That being said, a lot of tricks work better with center/extent instead of min/max, such as computing the AABB around an OBB or doing separating axis tests with abs() tricks. A bounding box and bounding sphere can also be stored together as center/extent/radius with only one additional value needed. Min/max works better for accumulation, though.