If the game has statistics for weapons, I prefer a limited number of weapon types with different qualities. Old School Hack is quite perfect for me.

tl;dr: Having no differences between things that are different, makes me not interested in a game.

I've always noticed that when I first start out considering playing a game, starting with when I only know the concept, I engage it as "oh, I have interest in playing a game about that". For example, I was drawn to threads about the game Zweihander, imagining a game where giant German two-handed swords would be an element of play. That sounds like it offers some satisfying heavy impacts, and lots of combat. Ok, I'm into that.

I've also noticed long long ago (age 8?) that there comes a point when, with most games, I grow disinterested. By age 15, I was pretty clear the usual cause: once I know how the game actually works, I start engaging the game at the the level of the rules, and if those rules are not like my ideas about the things the game is supposedly about, then I stop engaging the game as being about the things it pretends to be about - instead it's about game mechanics which work differently, and have little or no association for me to whatever the game represents. So for example when I read this thread and see it's asking if Zweihander should have any difference between a giant two-handed sword and a knife, and some people are saying something like "no, all weapons can do 1d6", then I am thinking Zweihander may be a strange name for an RPG about weapons that are all the same and do 1d6, or at least that the game is very unlikely to be very representative or detailed.

So why have "small" differences in stats for different weapons? Because if you don't, then they're not really different in the game, and it seems pointless or annoying to have them be called different things if they're really the same, unless they are really equivalent in use at the abstraction level of the game. But even then, the abstraction level shows the level where the game really lets you engage with the subject. So if you're not interested in the detailed situation of weapon differences, fine. I remain interested. If I'm a fighter, and the game doesn't make any difference between equipment, there's nothing for me to engage there, and I'm not interested in pretending to be someone whose interests and thinking is irrelevant and abstracted away - it makes me want to play games where those things are detailed, instead.

Weapons of Choice (or Necessity)

Historically, training seems usually to have trumped technology. Before the Romans, heavy infantry tended to favor spears rather than swords; maybe the former are better for citizen-soldiers, the latter for professionals. Tribes that didn't build cities tended not to field heavy infantry, but to adopt tactics suited to the weapons they used for hunting or protecting herds: the arms they knew how to use well.

If you haven't spent years learning to use a bow, you're probably better off with a musket. If you have spent years learning to shoot a bow from the saddle at a gallop, then any carbine short of a good breechloading repeater may be not much more than  a club to you.

Death of a Thousand Paper Cuts
"You can bring a knife to a gunfight, son, but if you bring a Form 2082(b) then it had better be in triplicate!"

A lot of things that could be deadly in a carefully planned assassination would not be sensible equipment for combat. In the interest of fantasy, some things that are more showy than practical might be rendered reasonably effective in the hands of a specialist gladiator or kung fu artist, but it does not follow that they should be so useful to others.

Plan B? What was Plan A again?
A soldier in any era might feel naked without a dagger. It's just the thing for when the scrap is basically a tumbling wrestle, as when you're pounced on by a beast fighting with fang and claw. It's advantageous for other special cases as well (stealthy ones for instance), and depending on design it might also be a fine working knife.

However, many generations of fighting men have found it definitely something to fall back on rather than to make their primary weapon. Even a great expert who sticks with knives probably does so  for the sake of a personal pleasure that matters more to him than tipping the odds in his favor. (It's like Celts going to battle naked, perhaps.)

Simple clubs are in the same category. A carefully shaped war club of hard wood may be in the same neighborhood as a mace with a head of stone or metal, but except for some sneaky killings something like a baton or baseball bat is not especially attractive unless you place a premium on taking captives. Even then, the Aztec would often use the flat of a stone-edged club resembling a sword.

Some weapons were carried mainly for throwing, and were probably in this category for hand-to-hand combat if the warriors typically carried something else for that.

Standard Equipment
Axe, mace, sword and short spear seem to have been about equally effective in trained hands. (A notable exception might be the Zulus' abandonment of traditional spear in favor of swordlike assegai.)

A thrusting weapon is better suited to close formations,while a swung one calls for more elbow room. Longer spears allow more ranks to get the point stuck in. Heavy swords and axes might suit warriors who are big on individual prowess and think little of unit cohesion.

Since FRP adventurers tend more to one-on-one duels, their weapon preferences might be different from those of soldiers bound for battle. For instance, the heavy two-handed sword might not be quite the rarity it is in proper wars.

On that pont, I'm thinking the greatsword might be -- in a master's hands -- as good as sword and shield in melee. Vulnerability to missiles would be a trade for a less encumbering kit, so you can outrun what you can't fight. It was deployed to make openings in pike formations, but so were sword and buckler men.

On a related note, the bronze-faced heavy hoplite shield could stand up to determined spear thrusts but had (perhaps by design) a grip that was not so good for fighting singly. The Roman legionary's shield was better for the latter, but definitely burdensome enough to make discarding it advisable for flight (or to pursue an enemy in flight). A lighter shield, of wicker and hide, could deflect or slow many incoming missiles while giving good mobility, but would not be so tough in melee. Macedonian pikemen had a smaller, shoulder-slung variation on the hoplite shield that let them use both hands to grip their weapons.

Special Weapons Section
Flails, bills, etc., were (a) modifications of peasant tools and (b) better for whacking the men on horseback than a hatchet. A problem with such a long weapon is that if the enemy gets past the business end, you've got to back up (or choke up) to be able to hit back. In a dungeon, you're not likely to have much room for that. If you've got a mass of guys in several ranks behind you, some of them can get in blows while you draw another weapon, but it's not really a very good setup for close quarters.

Even in the field, peasant levies were no match for phalanxes of well drilled soldiers able to maintain tight formation without stumbling over each other's weapons. Even crack pikemen would be hard pressed to keep gaps from opening on uneven ground. Getting outflanked could easily be disastrous; cavalry tended to be occupied keeping the enemy cavalry from making an end run.