The speed differentials on the autocross course aren't as severe as those at a track day. Most regional autocross aren't going to require a driver to slow from 150+ MPH to say ~90MPH (I'm estimating somewhat based on a ride in one of my former instructor's SN95 Mustang GT at Roebling). Basically, the kinetic energy generated by a car on a road course will be much greater than that generated by one on an autocross course.

Autocrossing is held by many to about as stressful on a car as one's daily commute. The speeds are similar and while things are happening in a shortened time frame, there's really nothing more severe than what would be seen in typical street driving.