Higher Qts = more control of the cone at Fs (Fs kind of becomes less irrelevenant the lower the Qts), tighter suspension and stronger magnet
Low Qts = less control of the cone at Fs, loose suspension and week magnet.
I don't know this 100%, but I think people forget about progessive spiders vs. stiff spiders. Think about it, a progressive spider can seem relatively loose on a high power sub with a medium sized magnet (like my Fi BL, goes in 5-8 cubes). But the woofer has an overall lower Qts, which translates in the sub being able to handle itself better than one with a higher qms. So it'll work in big boxes because the spider is stiff enough at a point to keep the woofer under control along with the medium sized magnet, but work in small boxes because the suspension is loose enough to move a good amount. Now my DC XL M1 has a huge magnet, and a progressive suspension. But because of the kind of oversized magnet for the power handling, it works optimally in small to medium sized boxes on higher power levels (5-6.5 cubes). It has a little bit higher qms. So kind of like this: same suspension (progressive) for both. But the magnet determines box size (in this case) because of how much more it impacts the travel of the cone. Big magnet, more moving of cone, smaller box. Slightly smaller magnet (and power handling, but not too much), a little bigger box.
With that being said, there are waayyyy more factors than that, it's just a way to think about it. Put a bunch of these style thoughts together and you can figure a lot out.