Pre-Seanchan capture, Egwene was fairly weak, and roughly equal to Elayne. Once they're back in the Tower, Elayne says she's stronger than anyone in the Tower (and Siuan confirms she's stronger than Liandrin, at least). This was the big jump, I believe.
After that point, I think Egwene kind of forced herself. I think the fear of being captured again led her to use the OP far more than the other women did. And remember: when Elayne and Nynaeve were off alone hunting the Black Ajah (and thus unable to channel very often for the fear of being caught), Egwene was in the Waste, and using the Power freely. That let her pull further ahead than the other two.