How Jesus died ? Is it important or not ? The most important thimg to know is :
he died on a cross and now how that cross looked like is a question of further deliberation.
Jesus was the final word of God in some sense as he was made a mediator of the New Testament and took the lowest place as God's servant . He was the last ! The last letter in the Hebrew is Tau : t - it resmbled in the old Hebrew a sign of a cross.And because of that it was fitting he died on a cross . If we put a pole and imagine a man hanging on it down and consider the inscription sign ( like a crossing bar ) above the head of the hanging person we see the shape of cross. If you don't agree with that you can add a crossing bar on which Jesus hands were stretched and yet we both can say Jesus died on a cross.
And we can see now it is not important how the cross was looking like .In both cases we see a cross.Jesus died on a cross in both cases.