Allow me to continue my analysis/rant of the TAR battles involving these two Forsaken. To a lesser extent, I think one can include Lanfear too.

If you look at it from a distance, Mesaana is a much greater dreamwalker than either Moghedien/Lanfear.

You will notice that Mesaana brings a mental battlefield into TAR for the first time, and Egwene starts to realize this as she's fighting her. On the other hand, Moghedien only uses physical means to fight in TAR, making her a massively inferior dreamwalker.

Moghedien creates false scenarios that try to snare Egwene, and she uses the Power in TAR to weave things and bind Nynaeve despite this being demonstrably weaker than most other techniques in this world. She openly spies on Nynaeve and the other Forsaken and hides like normal person, whereas even Bair can make herself look like a wall and blend in with her scenarios. While Moghedien can do impressive feats like easily cut away Nynaeve's shields or push Birgitte out of TAR, she relies on saidar to do so. She rarely, if ever, lets her thoughts stray to mental abilities, except perhaps when she threatens to make Nynaeve into a frog or pony in TAR.

Mesaana, on the other hand, doesn't even deign to enter into physical combat. She instantly enforces her will on Egwene that leaves her with a headache and almost gets her. If Egwene had been a lesser dreamwalker, it would have been game over.

The obvious reason is that none of this was thought of in the earlier books, and that BS introduced a new aspect of TAR that we haven't really explored. However, for the time being, I think Mesaana has been shown to be the greatest of the Forsaken dreamwalkers considering she uses the most logical tactic to overwhelm an opponent, which appears to work instantly.