My characterisation of the two types would actually reverse the top-down/bottom-up labels: type-A's seem to be dithering around in the details, trying to assemble something larger, while type-B's get the big picture, but loose focus as they zoom in on the details. In practice this explains the outward appearance: type-A's obsession with getting the plan right (because they are chronically lost), and type-B's rapid tinkering (because they never know if their crazy idea is going to work or not).
The two types struggle to connect: type-A just sees the B as a big mess, and type-B sees the A as technically correct but missing the point entirely.