Yes, applied force will be different. An axe has much more weight in a concentrated area at the end of a fulcrum. This means a much stronger impact per swing.
That’s why we chop wood or execute vie decapitstion with an axe (except for guillitine) and not a sword
For combat purposes – very different weapons used by different groups of people. I think with two professionals sword wins.
With two amateurs axe wins
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