I posted this on the Redshift thread, but it is applicable here. Note that the twin screw is for the Lysholm, while the Comptech and Jackson used a Roots style S/C.
http://www.8thcivic.com/forums/forced-induction-nitrous/70417-redshift-sc-coming-soon-2.html
The Lysholm supercharger would be a definite upgrade over a basic Roots supercharger. As was mentioned, adiabatic efficiency is greatly improved as well as the ability to run higher boost levels.
Many people confuse the twin-screw supercharger because they look similar to a roots supercharger, especially inside an engine compartment. However, they differ in that as a twin-screw supercharger draws air, the design of the rotors actually compresses air before discharging it from the supercharger. Because the compressing of air is done inside the supercharger, the twin-screw supercharger produces less heat than a roots supercharger.
Upgrades that many would be familiar with are the Whipple supercharger and KenneBell, both of which are famous on Mustang Cobras that want enhanced performance. Mercedes and Saab both use Lysholm superchargers as well.
I found this interesting info on a site comparing a Roots to a Lysholm:
Each of these systems offers some advantage over the other. Each has its srtong points and it's weak points. Here they are:
Roots: OK, we are talking about the MODERN Roots supercharger. A lot of vendors of other types like to compare using efficiency numbers from ancient GMC blowers. The modern Roots supercharger has a few big advantages. First it's the only style that compresses the air outside the unit itself. This means that when its bypass valve is open (standard equipment on all Magnuson kits) it's basically shut off. This means that any adverse effects on fuel economy or emissions during normal driving are negligible. Second, below 10 pounds of boost its efficiency numbers (i.e. power required to drive the supercharger itself and the discharge air temperatures) are really tough to beat. Third is reliability. The Magnuson supercharger requires almost zero maintenance. It only needs an oil change once every 100,000 miles and that's it! It has it's own reservoir so it doesn't heat up the engine oil. Fourth and perhaps most important is power. The Roots type supercharger puts out a lot of power at ALL RPM. Right off idle an engine with a Roots supercharger will typically have nearly full boost and massive power. This power increase will be fairly constant throughout the RPM range.
Lysholm: The Lysholm unit is very comparable to the Roots in most ways. It provides full boost from low RPM. Above 10 pounds of boost it's more efficient then the Roots blower, meaning it has lower discharge temperatures and uses less power to drive it. From a pure horsepower standpoint, above 10 pounds of boost the Lysholm is superior. From an "I actually plan to drive this car on the street point of view" it's not quite as good. The Lysholm has a few weaknesses. First, most street supercharger kits run 8 pounds of boost or less so unless you are talking about a custom built motor with low compression pistons, or you are willing to burn racing fuel, the Lysholm's high boost advantages are lost. The second weakness is that it compresses air internally. That means that a bypass valve can not fully shut it off. The result is your engine burns extra fuel to drive the supercharger at all times, even if you don't need the power. This also means that the supercharger is heating things up all the time which can result in a heat soaked intercooler, totally defeating the lower discharge temps. The fact that it can't be shut off with a bypass valve is the main reason the Lysholm design is not the design of choice among major auto manufacturers. It's worth noting that some attempts at shutting it off with an electronic clutch have been made, none have been successful in aftermarket applications.
This as well from RedShift:
1. What type of supercharger does RedShift use? Answer: We are going to offer several options. We will be offering Eaton Roots blowers as well as Lysholm and possibly Autorotor twin-screw superchargers.
2. Which is better, the Roots or Twin-screw supercharger??? Answer: Roots and twin-screw superchargers are very similar in look at operation, but the twin-screw charger is more efficient at making boost above 8 psi (meaning it creates less heat for the same psi boost). Both roots and twin-screw chargers are positive displacement pumps (meaning they displace the same amount of air per revolution), but only the twin-screw compresses air as it moves through the charger. The roots charger only moves the air from inlet to outlet (without compressing it internally); so the air is compressed only in the intake manifold downstream of the roots charger.
Bottom line is that if a Civic Si is going to be kept fairly stock with lower boost levels, a Roots type is the way to go. If the motor is going to be built up internally and with an injector upgrade, then the Lysholm might be the best way to go. Either way, we enthusiasts have more options now to choose from, which is always a good thing.