I will confess to approaching this subject from the experience of a ship's officer. That is not all to the bad, with exception granted to the notion of stinkpotters. What is apparent to me though is that, within our discussion, we are to some extent approaching things somewhat backwards. We should first approach such matters from the theoretical and then consider the practical.
Consider two opposing ideas. One holds that a stiff ship is desirable, the other that a tender ship is desirable. The stiff ship responds well to a press of canvas and heels much less under that load. She also has a very fast rolling period. The tender vessel will heel more readily and may well dip her rail much sooner under much less press of sail. So the vote goes to the stiff ship right? Not necessarily. We don't sail generally upon calm seas and the ship's motion cannot be ignored. This is particularly so when running. The stiff ship is much more prone to synchronous rolling given her already short rolloing period while the tender vessel will be far less likely to engage in such potentially catastrophic behaviour. All of which merely points out that things are not quite as simple as they may appear.
your original premise is incorrect. the difference is not tender vs stiff. it is form stability vs ballast. there are two ways to achieve a stiff vessel. one is to have a wide beam. this is form stability. the extreme version of this is the catamaran.
the problem with this kind of stability is that the more of it you have, the more your boat will tend to be stable when upside down. also, wide beam creates a situation where a boat reaches a sudden tipping point. it's very stable, up to a certain degree of heel. however, after that degree, the righting arm rapidly decreases and even passes by the CB.
and, finally, a beamy boat that manages to survive the first beam wave is easier capsized by the following wave, than the boat with a narrower beam, because it gives more surface for the next wave to push on....like a lever for the wave to use. the narrower boat has less surface for the following wave to grip and will tend to allow the wave to pass over.
however, there is another kind of stability: stability through ballast. this does not rely on form. if your ballast is a higher percentage of the over all displacement, your boat will be stiffer.
the capsize formula is set up to favor the narrower boat to the broader boat. that's why it compares displacement to beam.
now, there is a ballast displacement formula that figures how stiff your boat will be based on how much of it's displacement is ballast. the more of the displacement that is ballast, the stiffer the boat: ie the more it can stand up to it's sails. 35% is average stiffness. my boat has around 2 on the capsize formula and 125 AVS but it alo has a displacement ballast number of 50%. that means that, although it has good ultimate stability, it is pretty stiff, too.