Huh?

What exactly did Egwene do during the Seanchan attack that suggests that she possessess such superiour skill in battle-channeling as to counter Nynaeve's greater strength?

I thought she just used basic fireballs and lightning and that the reason she won was because of the link and the sa'angreal. I don't see any reason to believe that her fighting skills are all that better than Nynaeves.

I would say arguably the opposite. Nynaeve has actually been running around, fighting Moghedien and Trollocs with Rand and such, while Egwene has been playing politics. And that is without considering that Nynaeve has those new spiffy ter'angreal of hers.

Nynaeve would crush Egwene like a bug if it actually came to a duel, and if she really went all out.