I've only tried mclaren and F1 so far, and there was no difference for me in the feeling/handling. Tires felt like before with Q fuel and higher pressures, aka fastest on the first lap like they should, I'm guessing what you are experiencing is a slow tire-pressure buildup?
What car and pressures were you running? I run quite low pressures in the bigmac on race sets for ex and takes a few laps before pressures get up to operating area, car does feel a bit floaty prior to that.