Damping materials tend to be effective for low frequencies and sonic barrier materials tend to be effective for higher frequencies, with the crossover at about 500 Hz.

So, which is more effective if used alone in an aluminum chassis, a constraint layer damping material (Dynamat Xtreme, Second Skin Damplifier, and Sound Deadener Showdown CLD tiles are the only respectable materials) or a sonic barrier material that has a foam layer under the mass loaded vinyl layer, like the 3 layer Acoustipack?

The problem with using both a CLD and a sonic barrier material is that you don't ever want to risk damaging the constraint layer, which means to apply barrier material over the CLD you would want to use velcro strips and a composite material with no adhesive, like Second Skin Luxury Liner Pro. But then you are starting to make your materials rather thick.

There are composite materials that combine damping and sonic barrier - like Dynapad, but those materials are even thicker.

And now for a tutorial on the materials:

Damping materials are designed to absorb vibrations in the substrate to which they are attached. Constraint layer damping (CLD) material puts a layer of metal, the constraint layer, on top of butyl rubber. The constraint layer is essential to the physics, and aluminum is chosen because it is easy to cut, but ideally you want the constraint layer to match the substrate. Fortunately, high end computer chassis are aluminum. Installation of CLD is nearly permanent. It can only be removed by applying dry ice. Installation or removal makes no use of a heat gun; if someone talks about using a heat gun, they are a bottom feeder using roofing tar.

I want to emphasize, CLD does not work by mass loading. There are a lot of bottom feeders out there who use roofing tar as a damping material and most user commentary on the web for these materials is hopelessly ignorant. According to Sound Deadener Showdown, you only need to cover 1/4 of the surface area for CLD to be effective, and that's for car audio. PC cases are a lot quieter than that.

Sonic barrier materials are meant to absorb soundwaves traveling through the air. Fiberglass is superior to polyurethane foam, but foam is typically used because it is easier to work with. Outside of the computer world, there are barrier materials that can be purchased that are just foam, and some that are combinations of foam and mass loaded vinyl (MLV). If the MLV is present, there is always a layer of foam under the MLV and usually another layer on top of it, but not always. Only in the computer world do you see composite materials where MLV is on the bottom - Nexus Damptek and Acoustipack Lite. The 3 layer Acoustipack is a much more standard material, their claim that there is a patent pending is ludicrous. The purpose of the foam under the MLV layer is to sonically isolate the MLV from the substrate.