Pros and cons between turbo and supercharging

Also know that a supercharger takes power to make power while a turbo uses no power to make power.
Not quite. Laws of physics essentially says that something can't come from nothing. So the turbo cannot make power from nothing.

Supercharger takes power directly from crank. Turbocharger takes power from exhaust gas velocity and heat. Does turbo motor lose more power due to exhaust back pressure than supercharger cost in drag on the crank? Up to a point, no. While the fastest street cars in the world use turbochargers, the most powerful, fastest accelerating cars use rootes-type superchargers.

As far a lag goes if you do it right, you can reduce lag greatly.
Simplistically
1. There is a balance between the size of the turbo and volume it will put through. Small turbo: spools up quick, may not let motor reach full potential. Large turbo: takes more engine rpm to reach boost pressure (lag), plenty of compressed air on top end.
2. Keep the run of cool air tubing as short as possible. Reason? Smaller column of air to keep pressurized. An intercooler adds to length of column of air but cools charge.

Longevity:
Because of extreme heat of turbocharger, lubricants are stressed. When the engine is shut off, oil pressure goes to zero stranding lubricant in the shaft bearings of the turbo. These lubes get cooked (coked) in place. When the engine is re-started, fresh oil cleans it out. Sometimes the residue is broken up, sometimes it gets pushed up into bearings and seals eventually causing them to fail. The supercharger typically does not run nearly as hot, so much less bearing/seal issue. Solution for the issue: Let engine idle 3-5 minutes after hard run to let engine oil cool.