golfrewind.com

What exactly is the difference between the two?
(Other than Cross-hand= left hand below right)

Hitting cross-handed really takes a lot of the hand manipulation out of the swing. For many people, that is a source of inconsistency in the swing -- and if you think about it there are a lot of variables there... forearm rotation, wrist cock, release. Left hand low makes a lot of these occur in one position and one poistion only.

Another nice thing about cross handed is that it is much easier to set up with square shoulders. Many amateurs set up too open to the line, but left hand low forces you the reach down lower to get that left hand low and the address is naturally more square.

I putt left hand low, since I like eliminating all those extra hand variables. Julius Richardson in his book Better Golf even says "I believe 'left hand low' may be the better way to play the game -- but I don't teach it. It's too unconventional for people to accept." And this is probably it's greatest weakness, you'd find tips and training for the technique to be few and far between. I.e., many of the traditional fixes for a slice probably wouldn't apply to this method, since the swing is going to be significantly different.