I actually assumed, that her talking the way she does, not always being serious about what's going on etc. is just a form of fan service (fans would get crazy if they suddenly got 100% serious and calm Asuka) and decided to not draw any conclusions about her character from that.
That's why our impressions differ, I guess.
Her approach to battle hasn't changed, either, as she doesn't seem to adopt any form of strategy (she relies on Mari to support her in the space battle, and then yells for Shinji after that)
I don't think she could really do much about the situation she was in, considering all the limitations she had to face while fighting in space.
Besides, she actually *did* change her approach. She says something about "being brute" about it and then decides to use the arm gun to pull herself in to the tesseract. From this I concluded that the original plan was different.
I agree that she definitely doesn't behave like an adult in that scene, though.
Like I said - I blamed in on the fan service.
in the beginning she gets scared that her Eva will get destroyed while attempting to recover Eva-01's tesseract
It's pretty hard to not get scared in this situation. If her EVA is destroyed in space, she dies 100% unless Shinji decides to suck her in ;). Not sure if it has anything to do with being childish.
edit:
There are two other things that make me think about her as of someone more mature.
One is a subtle difference in her voice. Can't really tell what the difference is, but when she complains about Mari being late with the support fire, it reminds me of a commander informing his subordinate that he's made a mistake. I don't get the impression that Asuka is frustrated with Mari or something. I get the impression that she strives for perfection, wants her team to perform to the best of their ability, and thus communicates the issues she has with them. But the *only* objective is to do better next time. No hidden desire to boost her ego or something. Her allies play in *her* team now as opposed to NGE.
The second one is her eye-patch. It makes me think of her as someone battle-scared, and thus someone already experienced, who lost her innate innocence. It basically has the same role as Misato's scar.