there are pros & cons to both setups,
Turbos have lag, they break a lot easier, and getting everything tuned properly is more involved. You are also required to run an intercooler to crank up the boost. On the plus side, Turbos are more efficient, and there is almost zero parasitic loss with a Turbo, since it's driven by exhaust pressure. there's also more room for fine-tuning once everything is installed.
Superchargers are heavier than a Turbo, and there is parasitic loss, since most superchargers are driven by the crank pulley (or another pulley, or an axle, it depends on the kit). Those that are not pulley driven are usually electric, and those, while some actually work (like the knight engineering electric SC) require a bank of batteries and large electric motor drives, which eliminate parasitic loss, but increases weight, so it sort of balances out.
On the plus side, Superchargers are more reliable, less prone to breaking, and can use intercoolers to safely handle more boost just like a Turbo. most SC's don't require an oil line, since they're permanently lubed via sealed bearing cases, they can be clutch driven, so unlike a Turbo, they don't have to be running boost all the time, and there is no lag with an SC. Rather than making BOV/wastegate/boost controller adjustments to change boost settings, you can simply change a pulley on the SC to do the same thing (although a BOV/controller may be used as well in high-end setups). Instead of waiting for the motor to reach 2K rpms, you will get boost starting even lower in the revs, and down low, our cars need all the help they can get.
Yes, it's true that a lot of cars come with a Turbo from the factory these days, but the same is true for superchargers, Superchargers are also time-proven, they've been around longer than Turbos, so, as long as you buy from an established company, the results will be good, and the SC will be reliable, but the same goes for a good Turbo setup. It all depends on your personal tastes.