Jags superchargers are Eaton roots-type.
Delicious torque and make a perfect pairing with that 5.0 V8. Power delivery is linear but hair-raising.
Compare that to the twin-turbos of my brother's M6, power is extremely jumpy and peaky and it's hard to make the car feel graceful. It's fast as fuck, virtually no lag, but feels like some refinement is missing in how that power is put down. Having driven 500HP+ machines with SCs and TCs, my vote will always be superchargers.
That and they're far more reliable mechanically, easier and cheaper to fix.
Except that too much low end torque means you get wheelspin, and losing traction doesn't make you fast, whereas with a turbo you can limit low end torque if it spools fast and avoid problems that the Roots superchargers create.
Also, with a turbo you can adjust the boost curve using a 3 port boost controller, so you can avoid torque spikes etc. I can change the boost curve to anything the turbo can support. I can create huge torque spikes, make it perfectly smooth, hold more boost up top etc. BMW is retarded when it comes to doing turbo cars, so I wouldn't use them as an apt comparison.
For example, here's a stock 2013 GTR dyno:
It's at 3K RPM so most likely it's not spooled as fast as it could be, but see how smooth the torque band is? And that's a stock tune, aftermarket can be made even better.
Here's a stroked Evo powerband, you can see how the boost/torque curve is perfectly smoothed out:
Can't do that with a Roots blower, unfortunately.
I will say though that I fucking love Roots blowers though. The low end torque generated on a V8 is awesome. Positive displacement blowers truly live up to their name.
But turbos dominate overall for making insane power and being configurable for what kind of powerband you desire.