Brad,
If by "Class Module" you are referring to a class that only has Shared
members, then as the others have stated there is no performance or
memory-usage benefits.
However! the biggest benefit I see to using classes with Shared members over
Modules is encapsulation, you are "required" to qualify the name of the
class when you use one of the shared members, ensuring that you know were
that member is coming form.
BTW: You can relax this "requirement" by importing the class itself, which
then allows it to work like a Module for that source file.
For example:
Imports System.Math
Hope this helps
Jay