Turbo acceleration vs supercharged acceleration?

I owned a 05 Grand Prix GTP w/ comp g. It had a 3.8l OHV Supercharged V6 4spd auto, putting out 260hp and 280 lb-ft torque. When manually shifting the car via tap shift paddles I could never overtake another vehicle in 4th. I always had to downshift. I bought a 07 Saab 9-3 2.0T saloon. It has a 2.0l DOHC Turbocharged 4 5spd auto, putting out 210hp and 220 lb-ft torque, but if I want to overtake another vehicle in manual mode, I can do it in 4th or 5th and it accelerates faster than the Grand Prix did. Why is this?