Bill has never been written properly, in fact instead of him growing stronger because of the hammer he appeared to grow weaker. Let me explain; Beta Ray Bill defeated Thor without the hammer, and now he is barely able to keep up with Thor with the hammer. If Beta Ray Bill were written properly Superman shouldn't be able to stand a chance against him.
Why would I make this claim? Well when Superman briefly had possession of Mjolnir he was more powerful, in both strength, durability, and mystical might ref. JLA/Avenger.
I agree with Stoic. Odin thought Thor was getting big headed so he opened a portal to Asgard to find a worthy opponent to teach Thor a lesson. Odin then ordered them to fight without the add of a weapon, and Bill beat Thor. It was supposed to be a fight to the death, but Bill refused to kill such a worthy adversary for know real reason. After he received Mjollnir as a prize, Thor was furious at this, and demanded it back. Too keep the peace Odin then created Stormbreaker. So if people believe Thor could beat Superman then Bill could. So I say Bill.