Shorter tubes are always stiffer than longer tubes of the same type. Take a foot long pice of PVC pipe and a three foot long piece of the same diameter and thickness of PVC pipe, I gurantee you will be able to bend the longer one more than you can bend the shorter one, 'Tis the same for steel, or carnon fiber, or aluminum, or titanium, or unobtainium, or any other tube. Thus the shorter seat tube of a compact frame is stiffer than the longer seat tube of a regular frame - if they are made of the same tubing. That makes for a stiffer frame.

Throw in the longer seat post, and that may or may not end up with an overall bike that is stiffer than a regular frame with a regular-length seat post. But you asked about frames, not bikes. I'd guess - and it is only a guess - that the compact frame with a long seat post is still stiffer because seat posts are significantly thicker than are frame tubes. It also would not feel as good as a properly sized regular frame made of good steel, at least to my backside and legs.

As for why what used to be called "girls' frames" (as opposed to mixtes) were less stiff is because the top tube and the bottom tube met so close together on the seat tube, thus making for less natural leverage and bracing to resist up-and-down frame flex. Compact frames have signficantly more spread between where the top and bottom tubes meet the seat tube.