Early WRXes were notorious for having really laggy turbo systems, due to restrictive exhaust with multiple cats, and even a cat before the turbo (which is a really bad idea as far as response goes). I think that got at least a bit better in the later ones, but I'm not sure by how much.
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Most OEM turbos are on the small side, designed to produce lots of torque at low RPMs and with little lag. My old B5 S4 (2.7L, twin KKK K03s, stock), for example, made peak torque at like RPM, and it fell off a lot above (redline of ). Except for the slight whooshing noise, you almost couldn't tell that that car had turbos at all, and it made noticably better low-end torque than the 4.2L naturally aspirated V8 in the B6 S4 that I replaced it with.
Aftermarket turbo kits are usually sized larger than OEM applications, those K03s max out around 180-200 crank hp each, whereas the GT that Keith mentioned (which is about as small as you'll find in any aftermarket kit) is good for more like 250. The GT in my Miata is rated at 300, and in top gear on the freeway will go from vacuum to full boost in under half a second. In 2nd or 3rd gear (like at the autox) it goes to full boost in about as much time as it takes to get your foot to the floor.
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One other important difference in forced induction systems is how they respond to altitude. Positive displacement superchargers (and I think most traditional centrifugal ones, too) behave like naturally aspirated cars -- as the altitude rides and ambient pressure drops, the torque curve drops proportionally but stays the same shape. Turbo cars, OTOH, will spin the turbos faster to make up for the altitude losses to some degree. Raising altitude on a turbo will raise the boost threshold (minimum RPM to make full boost) and increase lag, but the peak power will not drop anywhere close to as much as a supercharged or NA car. If it's got MAP-referenced electric boost control and enough headroom in the turbo, it may not even drop the peak power at all.
The downside that I encounter for a turbo at autox is that the torque at a given RPM/TPS point can change as the boost rises. This makes powering out of corners a bit harder to get right than with a naturally aspirated or supercharged car, but it's far from an insurmountable problem.
Modern twin screw superchargers are the old Lysholm design realized with CNC machining. As such, they are a fairly recent innovation, going back to the s (the Lysholm design goes back to the 19th century). They are more efficient than Roots-type superchargers. One manufacturer claims 85% for twin-screw vs. 65% for Roots. Manufacturers of twin-screw (Lysholm) superchargers for automobile applications are Whipple and PSE.
They still have the drawbacks of the Roots compared to the centrifugal type. Centrifugal superchargers are easily driven by waste energy in the exhaust, meaning that you get "free" boost without stealing torque from the crankshaft. Even when they aren't, centrifugals can still reach 90% efficiency when matched for flow and speed...which are exactly the conditions in aviation...cruise speed and rpm are nearly constant (close enough to be near the sweet spot for centrifugal supercharger efficiency).
If there was no such thing as turbo lag, and if GM had not put Roots-type superchargers in mass production on diesel truck engines, the automotive world would have abandoned positive-displacement superchargers years ago. The hottest new development in automotive forced induction is the e-turbo, which incorporates a high speed (75,000 rpm) electric motor/generator on the shaft between the turbine and the centrifugal compressor. The motor can steal power from a battery to maintain shaft speed (and boost) off-idle, and can act as a generator, braking the shaft speed at high engine rpm and returning excess energy to the battery rather than dumping exhaust through a waste gate. You might think of it as electrical rather than mechanical turbo-compounding, with a computer rather than the mechanical design setting turbocharger rpm over the engine rpm range.
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