Flats are generally stiffer feeling because the outer wrap is a ribbon shape, not a cylinder one. So there is more edge-to-edge contact, and therefore friction, between the wraps. With round-wounds and the like, the contact area is much smaller, to they feel looser. (Core construction also makes a difference. So does material, thickness of core, thickness of wrap, other things, etc.). So YMMV.
P.S. I am happy to continue this conversation in the Strings forum. Please start a thread there and tag me if you want to continue.