The Brave Blade and the Chicken Knife can both potentially be the strongest weapons in the game (not counting the weapons in the bonus dungeon of the GBA version) if you use them correctly. They can be stronger than any of the Legendary Weapons and even stronger than the Ragnarok.
The Brave Blade has an attack power of 127 and adds +5 to Strength, but it loses 1 attack power every time you run from an enemy, eventually getting down to a minimum of 1. Running just a few times will make it weaker than the Ragnarok. However, if you do not run at all in the game, it has the highest attack power in the game.
The Chicken Knife starts out with 1 attack power and adds +5 to Speed, but it gains 1 attack power every time you run from an enemy. It also has a 25% chance of making you run from battle after you attack with it. Its maximum attack power is 127; after that, it will not get any stronger. Note that even though this is equivalent to the Brave Blade, the Chicken Knife's damage is calculated differently, and it will actually do more damage than the Brave Blade, making it the strongest weapon in the game. If you don't want to run from battle, the certain commands will let you attack without any possibility of running.
Most people recommend the Chicken Knife, partly because it lets you easily run from enemies that are otherwise difficult to escape. However, I rarely run from battle, and I don't like its side effect of forcing you to run when you don't want to, so I prefer the Brave Blade. Which one you use is up to you.