There's a lot of good info here, but there's also a lot of wrong info here.
There are 4 basic styles of superchargers:
Roots (Eaton M90/M115, etc)
Twin-screw (Whipple, Autorotor)
Centrifugal (Powerdyne, Vortech)
Axial (AxialFlow)
A roots blower is a positive displacement (meaning it creates boost 'instantly'

, and is one of the most inefficient designs there is. A roots blower will heat air up MORE than a turbo will. This is an effect of it's poor adiabatic efficiency (generally in the 50% range). They also don't compress air internally, they compress it either in the intake manifolds or intercooler piping/etc.
A twin-screw (Whipple, Autorotor, etc), is again, a positive displacement rotor. However, it has an internal compression ratio, and has a considerably higher efficiency than roots (72-80%), rivalling turbo's in adiabatic efficiency.
Centrifugal's are basically a turbo driven via a pulley, it's a turbine compressor with an internal compression ratio, they build boost expotentially, meaning boost will rise as RPM's increase (for example 0psi at 2k rpm, 2psi at 3k, 4psi at 4k, etc). They usually have similar efficiency to that of a turbo (68-75%). They're not very desirable due to their lag, which can be worse than a turbo application. They are beneficial though due to their compact size and ease of installation.
Axial flows are rather unique, they build boost by spinning an impeller, which draws air in, then stacks it on stationary blades (usually in opposing direction), as the air 'stacks' it compresses, then moves to another spinning impeller, and repeats the cycle, this is generally called 'stages', they require very high RPM and have exceptional efficiency, but aren't very common due to inability to make them very stable.
Now, it has been said that turbos create extreme heat and heat up the intake air more-so than a supercharger. This really isn't ture. The exhaust turbine housing will be the hottest section, and will heat up your engine bay, but this is preventable with a turbo blanket and some heat-wrap. As for heating the intake, there is very little heatsoak from the compressor housing to the intake air. The heat is generated from the compression itself, and is also a result of the adiabatic efficiency of the compressor. As mentioned above, most common superchargers (ie the roots blower), don't even come close to most modern turbos in efficiency (52% vs 79-82%), thus the superchargers outlet air temperatures are extremely higher which will result in higher pressures (so you'll see higher PSI on a boost gauge), while a lot of people are confused into believing that more PSI magically means more power this also isn't true. Your goal is more air volume, not pressure, and again, science class teaches us pressure is a product of volume and temperature, so it's not always good. Turbo's also allow easy adjustments to power, depending upon your boost controller you can either turn a dial, or simply press a button and instantly have an additional 100hp (if your turbo/fuel setup can support it), versus having to swap pulleys and possibly belts/etc with a supercharger setup.
As mentioned, turbo's suffer from lag. Lag can be easily combated by using a smaller turbine housing increasing velocity, however this decreases the maximum flow, so you can have a turbo that spools up rather instantly, however in the upper band it struggles. How much it struggles in the upperband varies depending upon engine size/compressor/etc. There's also various methods to increase velocity in the lower band then have a solenoid actuated 'flapper', that will then open another runner (increasing total flow), to have the best of both worlds (See the Mazda twin-scroll setups), or you can really get involved and use twin-turbo in sequential.
Anyway, they all have their place and their uses, most are personal preference. Turbo's generally provide much more peak power at the cost of lag/low-end, where most common superchargers are applicable for low-end and mid-range torque, but suffer in the high-end (twin-screw and axials work well in high boost high rpm applications, but are rather expensive compared to a similar turbo setup). And it's becoming increasingly more common for top drag cars to be turbocharged, if you happen to attend any local events you'll see many many categories dominated by turbo vehicles.
* This post has been modified
: 19 years ago