Arbitrum vs Optimism Fees

I read some articles about comparison between these two optimistic rollups. The main difference is that Optimism uses fraud-proof by executing every tx to ethereum, while Arbitrum uses multiple rounds of fraud-proofs by seeking to find disagreement in tx history. (Tbh I still don't get it)

But it said that Optimism has higher fees since it has to generate state roots on the chain for every transaction executed.

If that's so, why does currently Arbitrum has ~4x higher fee than Optimism?