Fuel needs air to burn, the more air you can compress into the cylinders, the more fuel you can burn to give you more power.
Superchargers are powered by the crank of the engine, so start compressing air whenever the engine revs, but also have a drag on the engine to power them. Turbo chargers use the exhaust waste has created by the engine operation to compress air, so do not have a drag on the engine to do their magic.
So, the tubochargers provide more power, but it is not done in a linear fashion, you usually have what's called a turbo lag, engine revs, produces lower power until enough exhaust pressure builds to run the turbo and bang you have lots of power. I am a big fan of naturally aspirated engines for feel, even if they make less power than super/turbo-charged engines, but I prefer the linear feeling of supercharged engines to the less predictable behavior or turbocharged engines.
Personally I think you suffer from American driver thinking, the power of the engine is not the most important thing for sporty driving, overall performance, suspension behavior and steering feedback are more important to me than these for driving enjoyment. You also have to remember that even the speed you get is not directly related to the power of the engine, but also to the weight of the car (power to weight ratio) and the transmission gear ratios.
That's why a Porsche GT3 with 'only' 530 BHP will kick a Dodge Demon with 808 BHP around any race track that does not simply go straight or ends in 1/2 a mile.