Web apps are are wildly inconsistent in terms of UI, but the user must understand them quickly (otherwise his attention span dries up and he'll go elsewhere).
The menu on hover has much better discoverability - when I see a button on a newly visited site, I have no idea whether it will pop a menu with more options (which I want), or it will take me away, destroying the current state of a page (including half-written comment) - which is obviously not what I want. It takes only a few percent of sites with a latter practice to make me fear clicking something I don't know - and intimidated user is not happy user.
By mouse, we explore stuff that's on the screen, hovering means 'I am currently looking at you', so it is pretty natural that the UI element show either what it does (a menu), or a hint (tooltip: this will delete the post you are writing).
On the other side, not reacting on hover is impolite - user asks what the element does, and you don't answer. People love to feel that they have control and know what's happening; every bit of feedback is important, and by not reacting on hover, you are wasting a chance to communicate.
In our recent desktop software (Outlook add-in TaskConnect), we went as far as putting the help tooltip to every active element, and setting the tooltip timeout to zero - therefore making it appear instantly. You can see a short video of how it looks in action. What do you think about that?
PS: In any case, menu should also always pop out on click, otherwise touchscreen users or keyboard people (including disabled users) wouldn't be able to use it.