AoK used the many of the same units throughout all the civs, the monk unit included. I suppose the current monk does well enough for the Western civs, but the monks in your picture would have been better for the Byzantines. Of course many of the civs shouldnt have those monk units either. And for that matter if your the Byzantines the monastery should not resemble a mosque.
Though I do think they could have done better with the Western monk, like the monks here. Notice the black habit of the Benedictines with the scapular over it,

Though if the idea was in fact to get the look of a Cardinal, I would have suggested a unit more like Cardinal Cushing here,
http://photos1.blogger.com/blogger/6322/78...ushing01rsz.jpgOr perhaps Cardinal Sarto, the Venetian Patriach in this photo and soon to be Pope Pius X,