Both are correct in their own way. :) I've been waiting... - implies that the action is not yet finish, the person is still waiting. I've waited... - implies that the action happened in the past and already ended. He's not waiting anymore.

If the person is still waiting, then I would prefer to say "I have been waiting here for hours". This sentence describes continuing action from the past up to the present time. Not using a progressive tense when it is appropriate qualifies as an error.

If you want to show your oponent how long did you wait, you should choose the first sentence.