I've seen way too many people on other forums ask this question and end up seeing WWIII happen...
I've learned that it comes down to personal preference. My little Supercharged Cobalt SS utilizes an Eaton M62 roots type supercharger. I love the instant torque that a supercharger makes, and the whine sound that it makes... But at least for smaller displaced engines like 4cyl for the most part turbos will make better power.
GM also dropped the LSJ for the LNF in the 08+ Cobalt SS, and it's making way better power stock vs the supercharged Cobalt SS.
Although as already stated the new TVS superchargers are making similar performance gains/mpg's as turbos traditionally have made. Not sure if any of you know this but Audi just recently signed a contract with Eaton and they'll be using TVS superchargers in their next RS6 and possibly RS4....
For smaller displaced engines such as 4cyls, and 6cyls, in my experience I've seen turbos make more power.
For V8's, roots type supercharger is your best bet.
If I had a V8 Camaro I'd go roots type S/C
If I had a V6 Camaro I'd go turbo............
They both have their pros and cons people. It's really just a matter of personal preference...