There is no one weapon which performs every single task better than every other weapon, no matter where it is used and what armour it is used with.
The Abyssal whip, Saradomin sword and Zamorakian spear are all highly effective, general-purpose, non-degrading melee weapons. The Armadyl Godsword is known for its powerful, accurate special attack, perfect for delivering a killing blow, while the Dragon claws are known to be effective for quick KOs in PvP. The Saradomin Godsword is known for its prayer restoration.
Perhaps the best overall stats go to the Chaotic longsword, which is rapid, very accurate and powerful; but degrades quickly, and costs a huge number of Dungeoneering tokens.