There is actually a benefit from perfect catches, but it's not obvious ingame. In addition to extra star tokens in the Stardew Fair, it also multiplies the skill experience received from catching any fish by 1.4.

It does not affect quality in any way.

There is actually a benefit from perfect catches, but it's not obvious ingame. In addition to extra star tokens in the Stardew Fair, it also multiplies the skill experience received from catching any fish by 1.4.

As of version 1.4, a perfect catch additionally increases the quality of silver and gold star fish by one level.