Yes, there is a difference in the spring rate, according to Hyundai. I've got a 2002 GT, and the ride isn't noticably rough, though, so I don't think the rate is much higher. According to most of the car magazines that have tested the Elantra GT and GLS, the GT suspension doesn't seem to make much difference in slalom or skidpad.
I've parked next to non-gt's, and by eyeballing it it appears that the ride height is about the same.