Turbochargers vs. Superchargers
Common knowledge dictates that the primary difference between turbochargers and superchargers is that turbochargers use exhaust gases to turn the compressor while superchargers use belts. While this is correct in broad strokes, in reality there are a few significant corrections to this broad view.

First, you have to realize that there are a few different kinds of superchargers.

The first is a centrifugal supercharger -- this is the kind that looks like the compressor of a turbocharger, with a pulley drive at the back in place of a turbo's turbine wheel and housing.

The second is the positive-displacement supercharger, of which the Roots (which uses two intermeshing rotors to pump air), Eaton (modified Roots), and Lysholm (twin-screw) superchargers are members. More details to follow...

Is either option better?

My opinion is: It depends

Turbochargers have a number of advantages over both types of superchargers. The first is that they are driven off of exhaust gas flow and heat -- while a turbocharger does restrict exhaust flow, the heat energy used to drive the turbine is "free". Conversely, a supercharger, which is driven directly from the crank, always takes hp from the engine -- as much as 30-40 hp even on a fairly small Eaton blower spinning at its maximum speed. The advantage is that there's no exhaust restriction caused by the turbine wheel. According to Mike Kojima in one of his SCC articles, for low boost setups the parasitic loss from driving the supercharger is often less than the power lost by reduction of exhaust flow (or alternatively, more pressure in the exhaust ports so that the engine has to work harder to push it all out)...but for high boost setups, a turbo will invariably win out with a properly-sized turbo that provides little-to-no excess backpressure.

There is also the issue of lag. Turbochargers have it...but, surprisingly, so do some superchargers! The centrifugal superchargers have a boost curve that varies roughly as RPM^3, and the pulleys are sized so that the supercharger reaches max boost at redline. The effect is that below redline, you ALWAYS have less than maximum boost (i.e. if your pulley is sized for 8 psi at 7000 RPM, then at 3500 RPM you'll have about 2 psi of boost!). By comparison, a turbo sized for 8-ish PSI of boost will be full-on rockin' by 3500 RPM, giving you a fatter powerband.

Positive-displacement superchargers don't share this characteristic -- their airflow is roughly linear with RPM, so boost stays relatively constant throughout the entire RPM range (if you ignore changes in engine VE).

There is also the issue of packaging. Turbos require you to modify the exhaust and intake sides of the engine to some degree; Superchargers only require you to modify the intake. But superchargers also force you to position the system in such a way that a belt can be run to drive the supercharger. In addition, positive-displacement superchargers are often designed to blow directly into the intake manifold (although some setups, like the Jackson Racing Miata supercharger [which uses an Eaton blower], have the blower mounted "remotely" and direct the air to the intake manifold with piping, like a turbo or centrifugal supercharger setup).

Last is the issue of thermodynamic (aka adiabatic) efficiency -- how much each compressor heats up the intake air. Roots and Eaton blowers are the worst, with efficiencies ranging from around 40% on the low end to about 60% on the high end. Centrifugal superchargers and turbochargers are the best (they're basically the same type of compressor), some with peak efficiencies around 80%. Somewhere in the middle is the Lysholm (twin-screw). Supposedly a Lysholm is very efficient (~80%) when the compression is internal to the supercharger itself...but some of the compression is invariably done in the intake manifold (like the Roots/Eaton blowers), which leads to lower overall efficiency.

Because of the efficiency characteristics, the Roots/Eaton blowers are the kind that, arguably, need an intercooler the most - but are often the hardest to incorporate due to the packaging of most setups for these types of blowers. That said, ALL forms of forced induction benefit from charge air cooling -- and if anyone tells you otherwise, you can laugh in their face.

So, the question as to which is the "best"...well, I think as far as flexibility goes, the turbo can't be beat. You can change the boost easily, and will provide a wide powerband. A positive-displacement SC would be a good choice if you want the "feel" of a larger-displacement motor, but ultimate power output isn't a priority. Centrifugal SC's...well, I think centrifugal SC's suck due to their power delivery curve, but that's just my opinion. There's no question that a centrifugal SC can make big numbers, but you have to wait till redline to get them...