Turbo vs supercharged, pros and cons considered, which is best.

Turbocharger:
Pros:
Significant increase in horsepower.
Power vs size: allows for smaller engine displacements to produce much more power relative to their size.
Better fuel economy: smaller engines use less fuel to idle, and have less rotational and reciprocating mass, which improves fuel economy.
Higher efficiency: turbochargers run off energy that is typically lost in naturally-aspirated and supercharged engines (exhaust gases), thus the recovery of this energy improves the overall efficiency of the engine.

Cons:
Turbo lag: turbochargers, especially large turbochargers, take time to spool up and provide useful boost.
Boost threshold: for traditional turbochargers, they are often sized for a certain RPM range where the exhaust gas flow is adequate to provide additional boost for the engine. They typically do not operate across as wide an RPM range as superchargers.
Power surge: in some turbocharger applications, especially with larger turbos, reaching the boost threshold can provide an almost instantaneous surge in power, which could compromise tire traction or cause some instability of the car.
Oil requirement: turbochargers get very hot and often tap into the engine’s oil supply. This calls for additional plumbing, and is more demanding on the engine oil. Superchargers typically do not require engine oil lubrication.

Supercharger:
Pros:
Increased horsepower: adding a supercharger to any engine is a quick solution to boosting power.
No lag: the supercharger’s biggest advantage over a turbocharger is that it does not have any lag. Power delivery is immediate because the supercharger is driven by the engine’s crankshaft.
Low RPM boost: good power at low RPM in comparison with turbochargers.
Price: cost effective way of increasing horsepower.

Cons:
Less efficient: the biggest disadvantage of superchargers is that they suck engine power simply to produce engine power. They’re run off an engine belt connected to the crankshaft, so you’re essentially powering an air pump with another air pump. Because of this, superchargers are significantly less efficient than turbochargers.
Reliability: with all forced induction systems (including turbochargers), the engine internals will be exposed to higher pressures and temperatures, which will of course affect the longevity of the engine. It’s best to build the engine from the bottom up to handle these pressures, rather than relying on stock internals.

Superchargers often go hand in hand with big V8s, and they’re certainly capable of producing big power.

As to which is better?
That would depend on you as far as what your planning to drive it for.