As powerful as a combatant Aang might be individual, he would be at a fraction of his strength without his two greatest elemental instructions, Toph and Katara. They have both contributed to the well being (and jeopardy) of the team, each offering invaluable skills in the Avatar's quest.
Their comparable talents beg the question; which is stronger among the two of them? It's time to shake off the dust and breakwater, determining the most capable bender between Toph and Katara should they come to blows.
10 Experience - Toph
Though Toph may have had a more comfortable life than Katara as the sole descendant of the wealthy Beifong family, her training is much more pertinent. She has mastered earthbending under the primal tutelage of badger moles, the original pioneers of earthbending (much akin to firebender relations with dragons).
Katara's training is much more insulated and artificial. She was one of Pakku's most prized students once he finally agreed to teach her, but their training would not simulate combat as authentically as the Blind Bandit's rumble in the fight arena. The aggregate of Katara's experience comes directly from the show, which gives Toph a massive advantage.
9 Mid Range - Katara
Katara's octopus stance grants her a considerable advantage in mid-range. Her arms can be formidable if she chooses to apply them, disabling Fire Nation soldiers with a single decisive slap.
Since oftentimes Toph's bending favors a direct approach (throwing a boulder into the air and striking it), it requires a notable amount of downtime to commence. Should Katara keep at a distance long enough for her tentacles to harry her without going too close to becoming vulnerable to the Blind Bandit's stone fists, Toph would be at a disadvantage.
8 Mobility - Toph
Toph and Katara may have comparable physical speed (with a slight advantage to the latter, given the former's blindness and age), though her ability to surf the floor beneath her feet gives her a boost Katara could not hope to match.
Katara may be able to replicate this feat in an aquatic terrain and later produce her own water through moisture in the area, but what she can create is not sufficient enough to ride at the speed Toph does. The most she could do is sporadically propel herself in a certain direction to avoid Toph's attacks.
7 Durability - Katara
Considering that Katara's bending does not innately make her sturdier, she is unusually durable compared to the rest of the cast. The water bender has walked off a direct boulder attack from Toph so potent the rock shattered on impact, though her greatest feat of stamina comes from the finale of season two.
When Zuko joined Azula's attack against Katara and the two blasted her into the crystals, it only took her a few moments to recover. Considering that the Fire Princess alone had attacks of enough caliber to disable Aang and Zuko in one shot, this insinuates how sturdy she really is.
6 Defenses - Toph
Katara may have innately higher durability than Toph, but the latter understands how to use her bending better to her advantage. With her feet alone, she can accumulate the earth around her into an efficiently compact shell able to withstand abuse from the elements and projectiles alike.
This shield is not flawless. Under enough concentrated elemental pressure (notably by fire benders), it can come apart and leave its wearer exposed. Nonetheless, it's far more useful than Katara's water, which relies much more on aversion than enduring the damage.
5 Reflexes - Katara
Toph's mobility may allow her to skate across the battlefield more conveniently than Katara, but her excessive reliance on the protection of earthbending renders her less able to use her reflexes instead.
Conversely, Katara's waterbending is potent enough to deflect firebending flames, physically contend with Azula's sparring, and even freeze axes in the middle of the air. This is especially useful against Toph's projectiles, as they are slower than many other forms of bending.
4 Creativity - Toph
Katara may have come up with the idea of turning her sweat into a stinky weapon when the two of them were imprisoned, but taking moisture from the air and bloodbending were both the suggestions of her morally grey mentor, Hama.
Toph's ability to blind her opponents through scattering dust in all directions and unbalance them through the vibrations she sends to the earth with her feet are much more convenient to a direct fight. It would provide an answer to Katara's dangerous octopus form as a means of offsetting her and disrupting her concentration.
3 Versatility - Katara
Katara possesses a weapon that arguably makes her the most deadly character in the Avatar universe; she is able to bend the blood of her opponents. This completely immobilizes them and places them in stasis, leaving them as helpless puppets at her mercy.
While she is reluctant to use this ability, it isn't beyond her. During her quest for revenge against the Southern Raiders, she openly practiced this technique against the man she thought was responsible for her mother's death. Bloodbending is a skill strong enough to disable the Avatar outright, who in turn defeated Ozai.
2 Strength - Toph
Relying primarily on the precision of her water and her impressive reflexes, Katara uses aquatic whips in dire situations which necessitate immediate physical confrontation. They aren't as lethal as her octopus form and have even been shrugged off against particularly robust pursuers.
Toph's stone fists afford no similar luxury to those who make the mistake of approaching her. Enhancing her strength with earthen fists, she can smash through her attackers with a punch strong enough to send several grown adult opponents flying in all directions. Should they come near one another, the fight would heavily favor the Blind Bandit.
1 Conclusion - Toph
As powerful as Katara's bloodbending might potentially make her, her reluctance to use it ~ especially against a friend ~ renders it virtually worthless. She and Toph may be able to conjure similarly devastating attacks on a grand scale, though large bodies of water for Katara to manipulate aren't as available to her.
Additionally, her water bending is not enough to crack Toph's armor-like Azula's oppressive force might. Without regard to who she is as a person, Katara has the talent necessary to defeat the Blind Bandit, but she does not possess the resolve to see it done.