Why do I feel like the motion ratio is different in the rear.
I hope I'm using that term correctly, basically the leverage the wheel has on the shock.

Is it different?

 

I assume you mean springs/coilovers when you say "same suspension". Sway bars are the other major element in suspension feel, and sway bars size/thickness has changed every couple of years on the s2000. So even with the same spring/coilover setup, you don't have the same overall suspension feel.

 

Just driving straight over bumps, the AP1 feels more compliant. Regardless of compression and rebound settings.

 

Sway bars affect vertical travel of the suspension, they're coupled to the lower suspension arms. When the wheel to travel up and down, you're flexing a big steel bar. That alone can cause something of a different feel. A 300# spring with a heavy, stiff sway bar is going to feel different than a 300# spring with a thin, flexible sway bar.

Another possiblity is that you have an 07. Somewhere along the line there were also some other tweaks made to control bump steer, your 07 may very well have that change as well. You may want to search for deatils on that change and see if that could be a factor.