In all likelihood, none.
While Bedrock will support different gas prices (using the EIP 1559 mechanism), with a mempool of pending transactions, that mempool will be private, so it will not open opportunities for frontrunning, sandwich trading, etc. The same economic and game-theoretic assumptions protocols on Optimism have now will still be correct.
Note that in the future we will consider making the mempool public, so this behavior may not stay the same in the long run.