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http://thief.wikia.com/wiki/Garrett

and most of us know who Ezio is

so who wins this fight?

The most skilled, quick and intelligent I imagine.

^ Wrong.
It has to be the stupid, slow and lackluster one who wins.

I'm going with Garrett he's fought more then just guards and swordsman

such as The Trickster from the first game

http://thief.wikia.com/wiki/Constantine

Does Ezio get the Apple of Eden in this fight?

And that is ?

'... it is capable of warping reality, creating illusions, starting and ending wars, and (provided it is used correctly) ushering in forced peace.'

Abilities shown: teleport(?), making exact clones of ones self, mass-scale mind control and controling the opponents body(?). Think there are more.

No, The one who wins in this fight is the one who does the best at karaoke night.