Aang is a master airbender as shown by his arrow tattoos. That said I would say that Tenzin is more powerful as we see him in Korra than Aang as an airbender in ATLA. Highlighting that in ATLA Aang has yet to reach his physical prime and be at his most powerful, I think 25 year old Aang is the most powerful Airbender by a mile in the universe, we just happen to focus on him when he is 12-14. It highlights that even technical masters of an element can learn and become more powerful, the experience part of mastery comes into play here.
Katara is considered a master Waterbender as we start Book 2 Earth. She and Aang had basically the same amount of training in waterbending, with Katara’s focus allowing her to surpass the fact that Aang finds it super easy to learn waterbending. The fact that Pakku was his teacher is really the only reason Aang is not considered a master waterbender at the start of Book 2, but after that he trains 1 on 1 with Katara who is the perfect teacher for him so we assume a full book 2 and 3 of 1 on 1 training are enough to have Aang reach the point of mastery. Katara is still a more powerful waterbender by virtue of her singular focus on that element and learning more of the styles. Both still masters, but are they at Pakku’s level where he is a technical master, but also has huge experience.
With Earth I consider Aang a master despite what Toph says because who is Toph comparing Aang to? Herself, Toph the most powerful earthbender in the world, with only Bumi in anyway a match for her. So her having such an unusual method of her own training (badgermoles) she is not the greatest judge of how masterful Aang is given that she realistically never had anyone in her own training to grant her the rank of master. Then outside of Bumi and Toph who is more powerful than Aang at Earthbending? I think Aang is better than Haru, Tyro, the earth rumble guys, most of the earth kingdom military guys we meet. No one stands out as besting Aang, especially given that Aang also has seismic sense which he used to defeat Ozai in the end, and his direct use of this in battle highlights him as a master.
Fire is the only element I think Aang is not a master of heading into the battle with Ozai purely down to the small amount of time he had to train. He is a skilled bender and once he learned from the dragons I think he developed very quickly to the point where he is a very good firebender heading into that fight, but not quite master level. I feel this is an element that he would need to do more direct training with Zuko or Iroh or someone else before he could be considered a master. We know there is a year after ATLA where we don’t know a lot of details about so he could have done some training with Zuko.
With Air, Water and Earth I think just time and his own training would make him much more skilled without needing to have direct learning sessions with Katara or Toph. Time to test and experiment with the limits of his abilities especially once he reaches his physical prime in his early-mid 20s. It speaks to how amazing most of our main ATLA cast is that they are in their early to mid teens and are considered masters and potentially some of the best ever benders of their element, without even being fully developed physically.