Actually, I would imagine that the helmet reinforcements were more due to the fact that the falx defeats energy redirection due to its tendency to 'hook' so you could probably jack up a helmet quite a bit through blunt force. Also note that they were strengthening the helmet with a simple brace rather than making it thicker and they added armor only to unarmored bits so it would counter the falx. So my feeling is that it was very good at getting a 'bite' and piercing tearing.

Kopis/Falcatta are swords that have heavy tips made to transfer impact and cut. Likewise, axes are smashing weapons with a blade unless you're referring to one of those Eastern dagger axes which are basically made for piercing..