The fact is they weren't better than any of them, and in fact, for most of history, the spear was the most common weapon on the battlefield. In the late middle ages this changed to the polearm(includes both warhammers and axes) and later the pike. Only the Romans used the sword as a primary weapon for their soldiers, and even then they also brought javelins and other weapons to add versatility.

The main advantage a sword has over other weapons is it's versatility. It can be effectively used to defend ones self, to cut, slash, stab, or draw. With all that and the fact that you can wear it on your hip without hindering your combat ability made it an ideal backup weapon. It's downsides were that it had limited reach (one handed versions which were more common for most of history) and was fairly ineffective against armour of any kind, where one of those other weapons mentioned above would be more effective.

So all in all you have a weapon not unlike the modern pistol, a sidearm, buy incredibly popular and useful despite the fact that it was not the most "powerful" weapon. That is not to say that there were not groups that used the sword as a primary weapon and that they did not have great success with it, but that the view that the sword was the ultimate weapon before the gun is simplistic at best and mistaken at worst.