There's no free tier that I know of. But, yes, it is drastically better, and it's specifically much less prone to hallucinate "proofs" that the previous answer is correct if you challenge it.
If you provide the inputs for some specific task where you expect GPT-4 to fail in this manner, I can give it a try.
But if anyone wants to give it to me for free, I would happily make a $1000 bet that I can get GPT-4 to make the same mistake.