If you view table legs as rectangular prisms, then they would be sharper, and thus be more likely to deal extra damage and cut your own hands as they became more masterful.
If you view table legs as cylinders, then there would be less accuracy, and more likely to drop the weapon, as the cylinder would be more smooth.
Also, weight should vary more as farther from masterful, because thye cuoold be extra large, or extra small.
In general, though, I would assume that masterful things are better balanced, which would make them at least slightly better weapons (even if that's not specifically what they're intended for.) Masterful things are also, in many cases going to be harder to break (not always, but often), which means you can use them to hit harder.
But, basically, this is just a rule of cool thing, to an extent. Beating someone up with a masterfully ornate table famed around the world as a triumph of tablework is just more epic than beating them up with a shoddy nothing-table.
And, additionally, from a gameplay perspective I think it's generally good to reward high quality in as many ways as possible. Having more things dependent on quality adds additional distinctions for objects that makes finding a high-quality thing more interesting to an adventurer, and makes raising highly-skilled dwarves more interesting in dwarf mode.
Of course, weight and material hardness should also play a major role... there's no reason the game can't consider many factors.