I'm assuming the one on the left is stock, and the one on the right is the z-offroad light? Did yours come with that screw and washer on it where the bracket goes over the post on the light? That is what I had to add. Mine did not have that, just the post with a hole in the middle, and the bracket kept popping off. I dug around in my "misc junk screw/bolt" bin and found 4 screws and washers to fit to keep the bracket on.
When I tried to install my OEM bracket onto the z-offroad lights, the hole in the OEM bracket was too large for the post on the lights. It looks like yours is opposite and the OEM bracket is too small? That's odd. The box on mine said something to the effect of "new style bracket", or something along those lines. I'll check when I get home.