Do all class specific resources (Fury, etc), slowly decay over time? If so, do they all decay at the same rate? So far I've focused on Barbarian, and I'm trying to understand how similar other classes are, since I party with them, and in the long run I'll play as them.
No. Only Fury decays over time. Spirit (for Monks) starts at 0, like Fury, but does not decay until used. All other resource pools are full by default and regenerate over time.