I don't believe that flats do put more tension on the neck than rounds for the same gauge/core size etc. But they do feel stiffer under the fingers as has already been noted. I had a set of Rotosound flats gauge 45-105 and they felt pretty stiff particularly for the A string.
Don't get me wrong, if I could afford something a bit bigger it would be a lot easier to shift band gear. But this is cheap to run and I can 'just about manage' especially as we aren't gigging that often.
With the back seats down I can fit my rack-mounted head, 4x10, 1x15, box of effects/cables and bass in my Nissan Micra (a tiny car). It does ride a bit low!