I have always been a fan of turbocharging. It just makes sense all the way around - except maybe for the negative of underhood (automotive) heat increase. Although, the new STS systems that are under the cars do away with that part, but I am sure it causes a tad bit more lag.
However, that being the negative part - all the rest is positive. Zero HP to drive it, since it uses waste to make power.
WEIGHT: No more added weight than a supercharger system, but I guess nitrous would have the advantage of just the bottle and a little plumbing for weight. Not much there.
EASIER ON PARTS: Supercharged HP comes in FAIRLY soft, depending on type of blower and how much drive it has or doesn't have. Nitrous just plain hits immediately, although you could run multiple stages and bring it in softer. Lots more $ for solenoids, lines, injectors, pills, etc, etc. Turbocharged HP comes in only as the engine generates it! So, there is no "surprise" for the engine. HP builds as RPM builds. No "shocking" of parts that so often causes breakage.