People overestimate the lethality of bullets. Most guns don't have enough stopping power to keep a seasoned warrior trained in sword combat from advancing on you. Hence why guns have 14+ clip sizes. So you can keep unloading ammo into him hoping he goes down.
It's safe to assume on that note, that the bigger the weapon or projectile the more damage would be dealt. A sword would certainly have more 'stopping power' in that.
You two are missing an important element to your claims, if we are talking non-lethal wounds (wounds that you can be brought back from, not necessarily even wounds that cannot even kill you.) then the argument could be made that an arrow is more effective than a bullet, or a sword as well. The reason for this, however lies in the fact that the wound was 'nonlethal' in the first place. The arrow pierces you and rips your flesh, or the sword does likewise, causing various tissue damage. While a nonlethal bullet most likely passed right through your body without harming internal organs or anything like that. There is no question of which weapon is more powerful as even a .22lr is capable of leaving the chamber with a force of up to 24000 psi (this is 40x the amount of power that professional heavyweight fighters can average with their fists) imagine that force hitting your unprotected body and you'll quickly realize that best case scenario would be for the bullet to pass completely through you without hitting vital organs or bones. (a .22lr would be the ideal round to get shot with, as it is small and narrow with little powder behind it so the risk of it ricocheting around inside your body are relatively small, thus it has less stopping power than most firearms. That said, the 22lr is responsible for more deaths statistically than any other caliber.)
To talk about lack of stopping power in this way, as if a modern firearm wouldn't be capable of 'taking down a seasoned warrior before he advances on you' is a complete joke. In a fight where a swordsman has to advance on you I'd be willing to bet money that the most badass swordsman in the world would die in a fight with your typical 13 year old YSSP member with a .22 colt cadet. With a firearm shot placement is king, and a couple of rounds center mass from a .22lr will kill a man quite effectively. Combine this with the fact that the swordsman has to advance towards the shooter in order to harm him and the outcome becomes even more obvious. There is a range at which a gun becomes relatively useless both overfar or overclose (The far distance varies with the firearm, obviously, as for the close-distance, which is all that matters to this discussion, if you have to take 3-4 steps in order to reach the shooter then you aren't close enough for a melee weapon to have the advantage yet. In fact at that point you are in the worst part of a killzone to be at assuming the shooter has his weapon trained on you you won't stand a chance.) Now when you add self-defense or even military grade cartridges to this picture a swordsman doesn't stand any chance at all. (I guarantee you, no one is going to keep charging at you after you've double-tapped a couple of .40 s&w bullets into him center mass, in rare cases a man may keep shooting at you for all of 2 seconds before the pain hits him, but no one can shrug that off and continue a charge. This says nothing of the superior range and stopping power that a dmr would offer.)
Guns don't have large magazines because single shots don't kill, they have them because at mid-long range hitting targets that are moving, ducking and trying to hit you first becomes really fricking hard, and running out of ammo in the middle of a firefight = death or capture. Arguing that magic surpasses guns or that in the realm of a video game swords can beat out guns is one thing, claiming that a sword has any type of real advantage over a gun in most scenarios is just foolishness. If it were even remotely true then soldiers would still be being trained in the weapons use, they aren't and haven't been for over 150 years now because they wouldn't stand a chance. (even in the rare instance that a melee weapon can gain an advantage, it would be much better to have a smaller blade such as a dagger that can be thrust quickly into an opponent at no range.)
