First of all why does an innocent man need to die for others(Sinners). Isn't this injustice ?
Moreover, what has Jesus Death brought for mankind ? Nothing, except the illusionary and hypothetical reasoning that he died for us , washed our sins and paid the ransom. Even if we accept this nonsensical human ransom theory, shouldn't have Jesus Death eliminated all sufferings and brought a Paradise Earth, right then and there ? When the price is paid, we get the benefit. That's how things work, right from the beginning.
Whether he died on a cross or a stake is another empty argument and reasoning based on a useless outcome.