With all the coilovers I've used, the ride gets stiffer the more you increase the ride height because the spring perches increase the preload on the main spring. A few coilover makers (Ohlins being one of them) change the way the ride height adjustment works so that doesn't happen.
And it goes without saying, damper piston travel is directly proportional to ride height. The lower you are, the less travel you have and the more time the car spends bouncing off the bump stops.