Turbocharging is arguably the best bang for your buck in power output for any engine and 3800's are no exception.

Some of the biggest benefits to turbocharging are:

• Minimal power necessary to drive the turbocharger (No it's not free horsepower)
• More efficient than most superchargers
• Wide variety in turbo size available for whatever power level you want to make
• Simpler and cheaper to add an intercooler than with supercharging.
• Easy to upgrade to a larger turbo down the road.

It's pretty important to keep charge air temperatures down on a 3800. Switching to a turbo makes this pretty simple and can easily net a lot of power just by converting a supercharged car to turbo with the same boost pressure. An intercooler is definitely recommended as well.

A 3800 with a stock cam and no engine mods can easily make well over 300 wheel horsepower with an intercooled turbo. It would require a lot of engine mods to do this with an M90 supercharger.
The highest horsepower builds all utilize turbochargers. Just take a look at the records page to see for yourself