Oh dear. Soft doesn't mean squishy and therefore more grippy; neither does hard infer cast iron properties.
It is highly unlikely, as good as impossible, that any difference might be detected in the effectiveness between different pad specs. It is entirely possible that the mere act of changing the pads eased the handbrake cable, compensator and caliper mechanism producing the improvement.
As someone who sprinted, raced and use my car on the road over many years, believe me, I have a lot of experience in this area. Changing pad specs will not have any affect on the effectiveness on the handbrake.
