I have two New Square Wires, and being as such, have no intention on buying the new Square Whisker anytime soon. The styles are very close to one another.
I've handled and tried on the original Whisker (I assume the Square Whisker feels the same), and it all comes down to preference. If you want a thick and more dense frame then the New Square Wire is the way to go. This can be lightened with the premium titanium variant. If you want the thinnest frame you can get before getting into Nanowire 4.0, then Whisker would be the way to go. Any of the three square styles that are available are very classy with a subtle aggressive look.