In comparing Aang to Korra in this stage of their training (which is, formally speaking, equivalent to Aang at the start of Season 3 minus all of the Avatar State stuff) this is the chief difference I see: Aang was always an airbender first and foremost. In virtually all of the major battles in TLA Aang defaulted to airbending through the "gaps" in the fight. So, for example, in a big waterbending showpiece Aang would perform some spectacular ice attack, his opponent would respond, and Aang would automatically defend with Air. When confronting a crowd, he would blast them back with Air. When taking put shots from Zuko he would ride his whirlwind around to escape or avoid... and so on. The other elements were usually additions to his basic defensive Air stance.
Korra has never been presented as treating Water in an equivalent way. From the very beginning she has behaved as if she were equally proficient in Water, Earth, and Fire. Thus she is not comparable to Katara, or Aang, or anyone else from the first series, since all of them treat one element as their only (or in the case of Aang, vastly preferred) style. She's a true jack of all trades.
I kind of wish they would address this, honestly; make her Water style the base that everything else builds upon. She should certainly carry a bottle of water with her, Katara-style.
