Question about marketcap for same token on 2 chains

Not sure if this is the right topic to post this or not but I needed some insight on what general opinion is about market cap for a token that is already on eth and now launching on bsc. There will be a bridge in between both the chains. So you suggest to keep the market cap same on both the sides of the chains even tho the bsc side launch is going to be a fair launch. So no pre sale or private sale. The token isnt distributed to anyone. Only the allocation will be for the team.

One thing is why I am confused about what marketcap to launch with bsc is the liquidity that we will be providing on bsc side. It will be 1/10 of the eth liquidity. So with the liquidity being different on both chains does it economics wise and tokenomics wise make sense to keep it at the same market cap or you think the market cap should be based of how much liquidity is being provided on each chain.

Again sorry if this isnt the right topics to post this. Appreciate your everyones input.