After getting to blaine and managing to get a 53 quality falchion frame the answer seems to be that Falchions get a +5% crit chance base and do slightly more base damage than a hawker for a bit less max damage, a tiny bit more base damage and less max damage than a hammerer, and much less base base damage and more max damage than a neo luger. They're pretty comparable to hawkers it seems, and a bit underwhelming. 5% more random crit chance might help if you're stacking crit% with stuff like steadfast aim, but for general combat you want a low AP weapon with reliable damage (and preferably burst fire), and another weapon with a large Critical damage bonus for using with aimed shot.
Attached a jpg I made of a 7.62mm and 9mm falchion, without gun nut, in case someone who has wiki access wants to add them in until someone manages to get a 50 quality one.
