I agree it is unfair to compare them, I also agree that Aang handled things better even at 11yoTotally disagree.
Aang was a goddamn 11 yo, and yet handled things way more maturely than Korra right from the start. Aang developed through the show, Korra didn't. Korra didn't lose her past selves right away, and in many ways her lack of basic maturity and common sense enabled to sever the connection. Korra had the help of a mature, powerful and influential bender, not a small group of teenagers.
TL;DR: The show's Korra sucks ass. In FET she's way better than in the show. Thanks God.
Aang was an 11yo air nomad where the past avatar existed 100s of years prior so Aang was the embodiement of the Avatar in everyones eyes and he had a lot of help from his friends, Korra on the other hand had to live up to Aangs legacy whilst it was still fresh in everyones minds, her "imaturaty" was basically her trying to live up to expectations and wanting to prove herself as the Avatar.
LoK was nowhere near as good as TLAB but it was still a decent show (best bits where the flash backs to the first avatar that gave a bunch of lore) and Korra did have some depth to her, the problem is that TLAB was such a well made show with some of the best charater development I have ever seen in any show, its kind of hard to follow such a masterpiece of story telling.