I think that "fed up with" is much stronger than the other. First phase means you're almost on the verge, but the second one simply shows that you're not really happy with a situation. Again, it's just my opinion :)

Not much if any difference as far I am concerned, either in meaning or usage.

You're right Yusuke, they do express the same idea. I'm not sure which is more common. Perhaps there are regional preferences. Don't forget to use 'being tired of' not just 'being tired' - if you don't use the preposition 'of' then it changes the meaning.

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