Here is the opinion of one Miata enthusiast from Miata.net forum:
Turbos work off exhaust gas, so when you are not in boost, your fuel economy will remain basically the same. Turbos generally make more power at peak, but the turbo must be spooled by exhaust gases before it compresses any air. This means you may have to wait for peak power. This is refered to as “turbo lag” and is not as much of an issue with modern engine management.
Superchargers are run off the serpintine belt, so they will constantly draw on the engines power to spin the scrolls, regardless of boost pressure or throttle position. This will hurt fuel economy more than a turbo. However, since the supercharger is always being spun by the engine, it can make peak power eariler with better responsiveness.
TURBOCHARGING: Higher peak power, but at the expense of instant response, best used in applications like drag racing, where the throttle can be kept wide open to keep an engine in peak boost. Heel-toe shifting/left foot braking can help keep an engine in peak boost, so that power output can be kept high even when the car is being slowed down.
SUPERCHARGING: Instant response, at the cost of peak power. Best used in applications such as autocross, where the driver is regularly relasing the throttle and wants instant power when coming out of a corner. This can be done with a turbo, but extra effort and concentration is required to keep the engine in boost; in contrast, just mash your foot in a supercharged car and full power is almost instantly available.
Personally, I like turbocharging. I love the idea of using waste (exhaust gas) to make power, now thats what I call a hybrid! Both methods work fine for street use, its your choice based on the info provided above. As for track use, each method of forced induction has its own benifits that make one or the other better in certain racing categories.