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:

• Nearly negligible power necessary to drive the turbocharger
• 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.

Consider that a stock L67 with an M90 produces 240 horsepower at the crank at 8 psi.
A turbocharged L67 without an M90 will produce 300 horsepower at the crank at 8 psi and can consistently reproduce that without as much heatsoak.

An M90 will also struggle to produce more than 10 psi without introducing a ton of heat into the intake resulting in knock retard.
A turbocharger tends to be more efficient at higher speeds so it can easily produce a much lower temperature air charge at higher levels of boost. Because of this it will require a lot of boost pressure to introduce knock retard on a turbocharged L67.

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