Right now Tuon certainly has much more power than Egwene. She's the absolute ruler of an empire, while Egwene has to take into account the Tower Hall. Under Egwene's direct control are only Tar Valon and the villages close by. Tuon has way more subjects.

In terms of military power, again the Tuon wins easily. She has the big Seanchan contingent which came with their ships as the core of the armies, which had come from the Seanchan continent, and are much more experienced and better trained that Gareth Bryne's army, the vast majority of which are raw recruits. Then they have the local forces of three countries under their command too. Even after they lost 100 000 strong force to Ituralde's army, they were ready to immediately gather a much bigger one. They have the advantage of the raken scouts.

In terms of number of channellers, it's anyone's guess how many damane the Seanchan have available, but since they've tested every woman in three countries, and have no doubt brought along a significant amount of them from Seanchan, and they also got 300 or so from the Shaido Wise Ones, chances are they should have at least 2-3 thousands of them. Even if they are somewhat less, they certainly are more than the number of full Aes Sedai Egwene has (something like 700-800 at most if all those with stayed away during the split had come back, which is doubtful).

Sure, if we add the possible allies of the White Tower, the situation chances. But Egwene has no control over the Aiel armies or the Andoran ones. She has significant political influence over the leaders of the Randland nations, and they will probably be allies of the Tower in case of a war with the Seanchan, but that's not the same thing. If Elayne thinks it will be better for Andor and Cairhien not to send their armies to help the White Tower, she will do it and Egwene has no way to force her to obey her demands. The same applies even more to every other ruler in Randland.

The advantage of Egwene is the political influence the Tower has, but it's at almost all time low due to the rise of the Dragon Reborn, the Tower split and the Seanchan invasion. Right now the only monarch whose support she can count on is Elayne, and even with her she can't really press the issue as the Amyrlin did in the old days, when there were no Dragon, Asha'man, Seanchan and Aiel to complicate the political situation. The Borderlander rulers, the closest allies traditionally to the Tower, left on their expedition without even informing any of the Tower fractions and are now most probably sworn to Rand. Illian and Tear are under Rand's control.