Nickson104 already wrote a pretty nice summary in his comment. I've been playing the game since early beta and I prefer the small AHs, so this might be a bit subjective, but overall the most important points have been mentioned already: A global AH makes it far easier for players to find the item they want at the cheapest price (which they usually want as well). A global AH makes grants a far bigger reach to single offers, so sellers will sell their wares faster as well.
