They both do the same thing but in different ways.
A Turbo uses exhaust gasses to spin the turbine so you will not come on boost instantly until some pressure is built as you move up the rev range. Bigger turbo = more exhaust gasses required to come on boost = more lag.
A supercharger is mechanically attached to the engine. Usually to the crankshaft. This means boost pressure is building from the get-go.
A Turbo will be easier and generally cheaper to get BIG power out of but unless you are looking for 400-500+ you can achieve the same power outputs with a supercharger and I, personally, think the supercharger approach is more suited to the high revving VTEC lump.
You retain the VTEC characteristics and throttle response but just add power everywhere on the rev range.
When/If I come to FI my S2000 in the future I will almost definitely be looking at superchargers.