Since I entered the debate, my opinion about the topic. Personally, I'd say that there's no "best weapon": a weapon is made (and efficient) for a particular purpose, against a particular foe, and according to a particular technological setting and culture. Each weapon is in fact the result of millennia of evolution through the art of war; the problem with fantasy games is then that they mix altogether weapons that historically never mixed, or became obsolete when other weapons or armours entered the game.
For instance, what RM2 calls the "shortsword" would match the swords used in antiquity (such as the Greek Xyphos or the Roman Gladius), used back then mostly as a secondary weapon (the first being the spear) and against somewhat primitive armours (since it was made of iron strips put on leather, I may consider the Roman segmentata to be AT17 but absolutely not AT19 or AT20). When the sword became the mostly used main weapon (migration age and later), such short swords became obsolete in favour of a longer and broader sword. RM2's broadsword may match the sword in the migration ages. As we entered medieval times, and armours became better and better, the sword evolved again, thought they first remained mostly for slashing use. RM2's broadsword may still apply for such swords, Oakeshott types X to XIV, when armours were more of the AT15-16 and AT18 type. Later, though, as armours became closer to AT20, slashing weapons became less and less effective, and swords would go more into thrusting types (Oakeshott type XV to XXI). There, we should use the Arms Law and Claw Law option for the longsword. After that, guns were created and armours became obsolete. What started to matter (again) was speed, and fast swords, starting the era of rapiers, foils and the like.
What was my point? Well, it's pretty meaningless to compare the efficiency of a shortsword, a broadsword and a rapier because each was appropriate in a specific time, according to exact factors. The same way, it would be meaningless to compare the falchion and the broadsword because, historically, each became prevalent in different regions (middle-west for the falchion, europe for the broadsword) for its specific region. Ultimately, I'd say that to find "the best weapon" for his game, a GM first has to determine his technological level (what kind of armours can be made?) and environment setting (obviously, people living in the middle-west never developed AT20 because no on would be able to stand being in it), try to match it his best to a period and location on Earth, and takes the most popular weapon of that period and place. Why "most popular"? Because when your life depends on a weapon, you take the best: in other words, there's a reason why a weapon becomes widespread, and it's because it was efficient, all things considered (i.e. another weapon may be more "powerful" but less versatile, etc.)
Using that reasoning, I'd say the spear+shortword is the best weapon in Antiquity times, the falchion in middle-west like settings, the broadsword during high middle ages-like settings, the longsword in later middle ages-like settings, and the rapier in Renaissance-like settings.
Now, if we're talking about pure game stats, basing my reasoning on the RMCI's strength and spread methods, I'd chose the warhammer. Here's my reasoning:
1) Remove two-handed weapons and polearms because of the two handed factor and parry limitation. For non-warriors characters, parrying is an absolute necessity and the shield bonus (even from a main gauche, not to have encumbrance penalties) cannot be ignored.
2) Take the lower strengths weapons: we get the rapier (91), the falchion (90), the warhammer (90) and the morningstar (88).
3) Take the lower spread weapons: we get the warhammer (25), the morningstar (30), the mace (30), the hand axe (30), the club (30).
4) Comparing both previous results, we keep the warhammer and the morningstar. Comparing both tables, the morningstar does a bit more damage for twice the fumble range. In fact, it has the highest fumble range, along with the flail (8 )!
5) 'Krush' criticals impair the opponent (with stuns) more often than 'Perforation' or 'Slash', going in favour of a blunt weapon.
6) So, the warhammer it is.
