Soon as they are engaged, right click again on their target and they will switch to swords...
As for your tests, AI most of the times recharges, or do something silly like keep on walking, plus you are sending AP units against non-armoured opponents in some cases: the results are flawned...
In EB there's no such thing as the "ultimate" unit, each has a field in which it excels, but against a certain opponent, even cheaper, it will utterly fail...
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