Tx fees: Grin vs Bitcoin

I am thinking about the tx fees recently.

Assuming that 1 grin = 1 btc, what are the tx fees of Grin and Bitcoin? Would the fees in Grin be lower or higher than in Bitcoin?

Or if we want to transact same value, say 100 dollars, of assets in each blockchain, what are the tx fees of Grin vs Bitcoin?

Thank you ahead.

Neither the amount of coins nor their purchasing power affect the size of a transaction.