For me there are a few key moments in these opening 2 episodes that really stand out and show why this show eventually became so popular.
The opening narration showing and telling you about the tragedy of war, a reference to the air nomad genocide and so much more.
Then one of the opening lines of the show being Katara calling Sokka sexist, what other Nick show would have the guts to have a character call another ain character sexist. Then to not vilify him for this, but rather show why he is this way (Being the only non child/not elderly male in the village, with no father or mother around to teach him) and set it up as an early issue for him to resolve.
I love how Aang immediately brings a little fun back to the SWT when they have had none for so long, while setting up the tragic idea that he is a boy out of time, 100 years have passes, no one he knows is alive (Until Bumi).
Then we have Katara, so hopeful and she just knows she can put that hope into Aang.
I just love the general idea of these 2 episodes, 2 siblings find the one person capable to changing the fate of the world and this meeting changes their destines.
Straight away you see that it is not just any other Nickelodeon show, this is different, it can be funny, but also serious, deep and meaningful and that is shown very well in these opening 2 episodes.
Really the only flaw with these opening episodes is that the humour just for these 2 episodes is a little bit too far on the typical nick show side of things (Snot jokes etc), but still has signs of the great Avatar humour we have come to love. The other thing is just that this is the only episode where Iroh firebends at the gaang, there are little things like this with Iroh in these first 2 episodes that I thing show that they were not exactly sure at this stage what their plan for him was. Thankfully next episode fixes this straight away.
Great episodes even 10 years on.