ok here goes with my unnecessarily long techno babble about newtons theorys and crap like that, but i know you guys probably dont want to hear it. so heres a (relatively) condensed version
supercharger- as discribed above, there are 2 major kinds of superchargers, the positive displacement and the centrifrugal. the p/d (or jrsc for jackson racing, the most popular p/d) isnt really very effective on small engines. most of the blowers you see on muscle cars are of this sort, but remember that muscle cars already have tons of torque needed to spin the screws, and their sheer size lets them push a lot of air. but hondas dont, and this design doesnt work nearly as well on small displacement, high rpm engines because the design hinders high rpm breathing. jr's own website lists a d16z6 motor as gaining 40whp and 20wlb/ft of torque, which is, well kinda pitiful compared to everything else out there. the torque is boosted on the low end though, so the car feels a lot stronger around town, but it just doesnt have the high rpm breathing that is the honda hallmark. if you get the endyn upgrades, it works a lot better, but they are expensive. this is a good choice if your looking just to add more hp than bolt ons, but dont want anything beyond that.
vortech, or centrifrugal s/c's work the same way as the compressor side of a turbo, but it is driven by a belt connected to the crankshaft instead of exhaust gases. this makes it less physically (or frictionally) efficient, but more thermally efficient. basically, it takes more power from the engine to drive it, but it makes far less heat both underhood and to the intake air, giving lower intake temps, more hp and less chance of detonation. it gives less hp per lb of boost as a turbo, but it puts less stress on the engine. it makes its power in a very linear way, meaning that your hp curve is going to look the same, its just going to be higher up in the scale. contrary to the jrsc, the vortech makes very little low end power, and very good top end. also unlike the jrsc, it can use a traditional intercooler. boost can be upgraded with smaller pulleys, but may people have problems with belts slipping at higher boost levels (the belt is smooth, not toothed). like the jrsc, it works good at stock boost, and even with upgraded boost, but you will not see the gains of a turbo, and dispite the claim of 'no turbo lag', it produces very little boost in low rpm, perfectly simulating turbo lag.
turbo- a turbo is the most popular application for boost. contrary to popular belief, most of a turbo's power does not come from the pressure of the exhaust, it comes from the heat exchange. i could go into the physics of it, but i really dont feel like it. basically, the bigger difference in heat between the exhaust manifold and the downpipe, the faster the turbine spins. as air cools, it releases energy. the faster it cools, the more energy gets released into the turbine. thats why putting a 3" turbo back exhaust on a turbo car has such a dramatic effect on performance. anyway, a turbo is the most energy efficient of the 3 major boost applications. on average, a turbo will "take" 5 hp for ever 100 hp it makes (meaning that for a theoretical 105 hp, you actually see 100 hp at the crank. this is due to the exhaust backpressure created by the turbine) where as the average supercharger "takes" 30 hp for every 100 it puts out (130 theoretical hp, but you see 100 at the crank, the 30 is necessary to drive the s/c belt). a turbo also adds a lot of heat to the engine bay, and even with a large intercooler, it injects pretty hot air into the intake, reducing efficiency and increasing the chance of detonation. all air, as it is pressurized, heats up. s/c's only add the heat from this pressurizing, where as the turbo also adds the heat from the exhaust. exhaust gas temps can exceed 1800 degrees, and both the turbo housing and the turbine wheel get very very hot, heating up the intake charge more, in addition to the heat from pressurizing. a turbo, no matter how small will have a certain "boost threshold" which is the point at which your intake manifold goes from being in a vaccume to being under boost, and some turbo lag, which is the time between when you floor it and when the exhaust gases are heated sufficiently to spin the turbine wheel, the wheel spins the compressor, and the intake charge is compressed enough to satisfy the demand for power. the two terms are different, and i know its hard but they are unique and must be kept separate. a properly sized turbo ( for stock boost levels, something like a t25, 14b or t3) will have a low boost threshold and little lag, but will make much higher gains top end than either s/c will.
the choice of s/c and turbo basically comes down to the user. if ultimate reliability is the highest goal and power production is second, than there is no contest- get a supercharger. which one you get depends on where you want your power- down low or top end. if you want higher power production, more adjustability (s/c's boost is set with pulleys, and is not variable from the car, where as a turbo is adjustable with a boost controller) then go for a turbo. psi for psi, it will make more power than a s/c over a larger rpm range. hope this helps.