One of the minor beauties of cross-draw carry is that it makes a gun grab slightly less likely. From the direct rear, a grabber has to use his left hand to manipulate the holster release stuff, then would have to turn the gun around in his hand to operate it.
From the front, the carrier can more easily fend off a grab both by covering with his left arm/hand, and by defending with his right arm/hand. Besides the additional warning.
There are other advantages, such as easier retrieval from a sitting position, as in driving, even with a seat belt on. In addition, you don't have to crook your drawing arm up too high, almost to the limits of the elbow's bend angle.
There are some slight disadvantages, such as the fact that you have to swing through the target horizontally as opposed to the longer target area in swinging through vertically, as well as some others.
Frankly, excepting for the use of a drop holster, I don't see why right-handed folks carry at around the 3 o'clock position.
Cross-draw for the win !
Terry, 230RN