Neither of those formulas strikes me as reasonable. For example, enter a temperature of 0F and a windspeed of 0 mph. The windchill index at that site comes out as 48F (old formula) or 36F (new formula). Sorry, but if I go outside on a 0 degree day it doesn't feel like it's either 36F or 48F just because the wind isn't blowing.

The site needs to add some input validity checking. The NWS formula is based on some curve fitting that's only valid for certain ranges of the temperature and wind speeds. Specifically:
-50F < T < 50F
3 < WS(mph) < 110