With Katara and Azula, it is clear that Azula had more power, although you must keep in mind, while she was exhausted and weakened along with being insane, Azula was still enhanced by Sozin's Comet and Katara couldn't use the full power of her bending abilities as the full moon wasn't out. Taking previous feats into account, it's fairly reasonable to assume that without the comet, Katara and Zuko/Azula are even.
In the conclusion of Book 1, "Siege of the North", Zuko infiltrated the Northern Water Tribe, trying to kidnap Aang while his soul was in the spirit world. Zuko and Katara were even, having the advantage with their respective points in time, Katara having the edge under the full moon, and Zuko overpowering her when the sun came out.
The final chapter of Book 2 was one of the most memorable, respected, and well-written episodes of ATLA to ever exist, "Crossroads of Destiny." Within this episode, there is a climactic battle in which Aang and Katara battle Zuko and Azula. In this battle Katara is able to make tentacles made of water around her arms that are able to overpower Azula's blue flames.
After this, Katara has done various things to exercise her bending abilities. She put out a fire caused by a meteor, assisted in the battle against Combustion Man, and most notably proved herself to be a stronger and more capable waterbender than the water and bloodbending master, Hama.
In the final episode of Avatar as a whole, Zuko and Katara confront Azula. After Azula cheats in order to take Zuko out of the picture, she goes after Katara. In part of this confrontation, Azula sends a bolt of lightning at Katara, which she counters with a wall of sorts made of water. Because I'm such an Avatar and powerscaling fanboy, I've looked over that quite a few times. What I come to realize, watching the animation, is that Azula's lightning blast doesn't completely destroy it, but rather, it penetrates a significant portion, and the heat of the lightning causes the wall itself to dissipate.
So yeah. I would say it's fair to assume that Katara has been comparable to the level of Zuko and Azula, and has been for a decent portion of time.
Note: It should also be noted that her powers are somewhat based on her emotions. For example, she inadvertently destroyed (in calculation standards, fragmented) an iceberg in the very first episode out of sheer anger. Or for another example, she first used bloodbending in the conclusion of her fight with Hama out of sheer desperation of stopping her from manipulating Aang and Sokka and killing the avatar.