This is currently intended. Hatred regenerates itself over time, while Fury does not. If you are not in combat, Fury can drop down to 0 while in game as well. Also, the Barbarian abilities that generate Fury generate a lot of it at one time, where as the Demon Hunter skills build up a little at a time.
You are more than welcome to post feedback about this in the Beta Feedback forums, but as of right now this is intended because the Barbarian has many tools to generate a lot of Fury very quickly while in combat, where as other classes need to be a bit more tactical in how they build up their resources.
Fury vs. Hatred Regeneration