There's nothing new about boosting an engine for more horsepower and torque; turbochargers and superchargers actually date back to the turn of the 20th century. After shrinking enough for use in mobile applications, turbo-superchargers saw use in high altitude aircraft, where they compressed air in the engine to prevent power loss at high altitude. There's no doubt about it; boost will add power, but it might not be in as linear a way as you might think.
Superchargers run off a belt on your crankshaft, and turbos get their power from high-pressure exhaust gases. Other than that, they're identical in terms of function. Turbos and superchargers are air compressors that shove more air into an engine than the pistons would be able to suck in on their own. More air equals more oxygen, which means that the engine can burn more fuel and make more power. However, compressing air also causes it to heat up, reducing its oxygen density and increasing the odds of detonation in the cylinder. So the trade-off is that you do get more horsepower out of the same displacement, but eventually you'll reach a point of diminishing returns where boost pressure is concerned.
Boost and Horsepower
The general rule of thumb is that, not accounting for temperature-induced power losses, a turbo will increase horsepower by about 7 percent per pound of boost over a naturally aspirated configuration, and a supercharger will increase it by 5 or 6 percent per pound of boost. The supercharger's return is a bit lower because it takes power from the crankshaft to turn the compressor, which a turbo does not. If your example engine makes 150 horsepower naturally aspirated, then you can estimate an extra 10.5 horsepower per pound of boost with a turbo and 7.5 to 9 more horses for a supercharger. If you're running 8 psi of boost, then that's an approximate 234 horsepower with a turbo and 210 to 222 with a supercharger.
Adiabatic efficiency is a measure of how well the supercharger or turbo compresses air without causing it to heat more than absolutely necessary. The compressor's AE range depends upon the ratio of pressure it produces to the amount of air it can flow, and all compressors have a "sweet spot" where they function at maximum efficiency. Manufacturers test compressors to produce what are called "boost maps" -- charts that index a compressor's efficiency. Small turbos will tend to be very efficient over a wide range of boost pressures, but have limited airflow. Large compressors offer more airflow, but tend to have a narrower efficiency range.
Adiabatic efficiency and efficiency ranges are crucial where turbo selection is concerned, since power drops by about one percent for every 10-degree Fahrenheit increase in temperature. So, if your compressor drops out of its efficiency range and starts producing 70 degrees more heat than it needs to, then you're effectively down one pound of boost's worth of power and you decrease the engine's octane tolerance. This point of diminishing returns tends to happen around 7 to 8 psi of boost, so consider an intercooler mandatory for anything over that.
The Golden Rule of Turbos
With all that said, here is the single most important consideration where turbo engineering is concerned: boost itself is irrelevant, airflow is everything. High boost pressures mean nothing if you're only using them to compensate for terrible airflow through the cylinder head, and your quest for power will ultimately hit a thermal wall if you don't build the engine itself first. Airflow through your cylinder heads, and intake and exhaust manifolds will have an exponential effect once boost hit the engine, so building an engine right in the first place will allow you to run a few pounds less boost while maintaining the same horsepower and torque levels. That means a cooler, longer-lasting and more octane-tolerant engine that still produces the power you want.
Applying the Golden Rule
Consider this scenario: A novice engine builder and a seasoned pro are competing to do a turbo buildup on an engine that makes 200 horsepower in stock form. The goal is to make 500 horsepower. The novice's approach might be to simply bolt a massive turbo to the engine, one with enough juice to produce 21.4 psi of boost pressure (200 x 0.07 = 14 horsepower per pound of boost). These extremely high boost pressures would necessitate a massive, slow-spooling turbo, an intercooler, 114-octane race gas and maybe even a water spray system to keep the engine together. The more experienced builder would port his cylinder heads, install a larger camshaft and bolt on a free-flowing intake to bring naturally-aspirated power up to about 250. Now, horsepower per pound of boost is up to 17.5, so he only needs 14.2 psi of pressure to get to 500 horsepower. From here, the wise builder can use a quicker-spooling, more efficient turbo, a smaller intercooler to enhance boost response and can run his beast on the street with 93 octane fuel. Even better, if said builder wanted to run race gas and crank the boost 21.4 psi for track day, he'd end up with an extra 126 horsepower over his bolt-on wonderboy rival. Feh...kids.