Matt,

You might want to take a gander at this article. I'm not sure what you
mean
by slow corrections, but evidently S-TEC (taken with a grain of salt) has
optimized the corrections, as well as smoothed them to avoid overstressing
the aircraft in turbulence.

See Pages 6 & 7.

http://www.s-tec.com/pdf/autopilotbook.pdf

....but the S-Tec related Meggit line of products just offerd an autopilot
aimed at the multi/turboprop market, and it's attitude(position) based.

Seems the realized that a rate-based auto is not on par with the airplane
when installed in, e.g, a fast single-engine turboprop, just as Michael
said.

Regards

Kai