What can irritate me about the menu button is that you don't know whether there's anything available unless you press it. It is particularly annoying when you think options should be available and they're not (or they're not where you think they should be).
Honeycomb cleans this up with the action bar. The action bar is on top of the screen and contains whatever actions are currently available. If there are more actions available than what can be fit in the bar, then they get put in a visible overflow menu. The key improvement here is that the action bar is (almost) always visible, so you can quickly glance at it to see what actions are possible (rather than the more complex menu-button flow).
Honeycomb cleans this up with the action bar. The action bar is on top of the screen and contains whatever actions are currently available. If there are more actions available than what can be fit in the bar, then they get put in a visible overflow menu. The key improvement here is that the action bar is (almost) always visible, so you can quickly glance at it to see what actions are possible (rather than the more complex menu-button flow).