LAG
Definition: Within a turbocharger's operating range, lag is the delay between the instant a car's accelerator is depressed and the time the turbocharged engine develops a large fraction of the power available at that point in the engine's power curve.

Now it's time to evaluate the turbocharger versus the supercharger according to several important factors.

Cost
The cost of supercharger and a turbocharger systems for the same engine are approximately the same, so cost is generally not a factor.

Lag
This is perhaps the biggest advantage that the supercharger enjoys over the tubo. Because a turbocharger is driven by exhaust gasses, the turbocharger's turbine must first spool up before it even begins to turn the compressor's impeller. This results in lag time which is the time needed for the turbine to reach its full throttle from an intermediate rotational speed state. During this lag time, the turbocharger is creating little to no boost, which means little to no power gains during this time. Smaller turbos spool up quicker, which eliminates some of this lag. Turbochargers thus utilize a wastegate, which allows the use of a smaller turbocharger to reduce lag while preventing it from spinning too quickly at high engine speeds. The wastegate is a valve that allows the exhaust to bypass the turbine blades. The wastegate senses boost pressure, and if it gets too high, it could be an indicator that the turbine is spinning too quickly, so the wastegate bypasses some of the exhaust around the turbine blades, allowing the blades to slow down..
A Supercharger, on the other hand, is connected directly to the crank, so there is no "lag". Some superchargers are able to produce boost at a very low rpm, especially screw-type and roots type blowers.