That's because you narrow down "dreamwalker" to "who would win in a fight in TAR".

Mesaana has a stronger personality than Moghedien, it's not really difficult so far. She's also more clever, and a faster thinker, and she doesn't shy from fights, so she's got experience.

I would say Mesaana got involved in what was easily the most impressive battle of wills in TAR so far. I'm not as much impressed with her skills in TAR than I was underwhelmed by how Egwene initially approached the fight (but then, Egwene has basically zero fighting experience, except with the OP.... same for the WO dreamwalkers).

I wouldn't say that makes her a better dreamwalker. She is experienced enough with TAR and its characteristics to stand her own in a fight there. She is far more daring than Moghedien, so it's really not surprising she dated fight... Moghedien avoids face-to-face duels, normally. She makes a speciality of traps, and she's obviously not an impressively intelligent fighter.

That doesn't mean Moghedien or Lanfear aren't much better skilled or knowledgeable in TAR, more accomplished dreamwalkers, than Mesaana.

Moghedien sure let the a'dam capture her, and that looks like a massive mistake, but then breaking away meant facing Nynaeve head-on, and Moghedien avoids fights, except when anger blinds her to her fears. She knew how angry she's made Nynaeve, and how strongwilled Nynaeve was, which compensates in part for her lack of TAR skills. Better be captured than be killed in a direct fight, Moghedien might well have thought. Her previous encounters with Nynave had not really gone that well... She might have been waiting for the perfect opportunity to escape when Nynaeve's attention slipped, but Nynaeve outwitted her first with the forkroot. Nynaeve also didn't make Mesaana's mistake with Egwene. Once she'd taken Moghedien by surprise, she held her through sheer force of will.

Mesaana had more courage, her confrontation was more clever at first but was entering a direct duel of wills with a natural and trained Dreamwalker like Egwene so wise? Its not like Mesaana had no idea of Egwene's strength of will... Moghedien survived her fights, in a shaming way, but alive and well. Mesaana boasted about her skills and knowledge, but she left Egwene the fatal chance to clear her head, think and strike back. In TAR - where control is everything - it's a good way to get killed or destroyed... and that sounds like a fairly average dreamwalker's mistake.

I'm still waiting for Cyndane. I'm pretty sure Lanfear is much nastier in TAR than Mesaana, combining her intelligence, her daring and superior TAR skills. The Shadow's three best dreamwalkers are still alive, I think...