I've ridden in both turbocharged (Lancer EVO VIII, Eclipse GSX, and lord knows what other random turbocharged cars) and only one supercharged car (high 12 second Grand Prix GTP). If I had the choice...and the extra cash, I'd go with a turbocharger. I'll explain my own personal beliefs:

Since a supercharger is belt driven, it basically kills horsepower in order to make it, causing the engine more strain just to spin the turbine. You are boosting as soon as you hit the gas, with a small enough pulley, you can be boosting at idle so its all there ready for you as soon as you accelerate. Only problem is, if you plan on building an all out drag or race car, a supercharger isn't the way to go. A supercharger will eventually hit a wall when it comes to how much boost you can push outta it. The only thing you can do with a supercharger is swap the pulley, given you have an adequate exhaust and an intercooler when the boost starts getting a lil high.

With a turbocharger, the sky's the limit when it comes to boost. With a well built and constructed turbo kit with a turbo size suitable for your car, you will experience little turbo lag, not enough so that it'd become an issue. It is more difficult to maintain a turbocharger and once the boost gets high, you should really invest in an intercooler. I personally would take a turbocharger over a supercharger, but either way, both provide good power and make a badass sound.