Out of curiosity, when the credits rolled for Episode 8, how did each of them grow as characters compared to how they were when Episode 7 ended?
And let's compare that to how the Mando is/was after Chapter 1 alone just to keep it within topic.
More or less the ways I described in my original post. I'll keep it simple by focusing on Kylo Ren as he has the clearest sign posts in his character arc.
Kylo Ren in episode 7 is pretty simple. He's angry at his family for reasons that aren't clear to us, he appears very loyal to Snoke, who seems to his only strong relationship since he cut ties with his family, and he struggles with adhering the Snoke's doctrine (which we see when the decision to kill his father is difficult for him).
Thats pretty much everything meaningful about Kylo Ren in TFA.
TLJ has to do some heavy lifting to further reveal his character to us, so we learn that Kylo Ren was betrayed by Luke (from his point of view). This leads us to understand where all of his anger has come from and why he would have been motivated to turn to Snoke. This is pretty foundational: Kylo turned to Snoke because he felt Luke and the doctrine Luke represented had betrayed him.
In TLJ, in contrast to TFA, we can see that Kylo's relationship with Snoke is starting to fray. Kylo is frustrated with Snoke. At the same time, he's building a relationship with Rey. This guy is pretty desperate for human connection at this point and the only even remotely positive relationship he has is with Rey. Snoke makes matters worse by gloating about how he manipulated Ren throughout this ordeal and that Ren is merely his slave.
So now Ren feels betrayed by another mentor representing another doctrine. He decides to hell with all of them; he's going to kill Snoke, and he offers Rey a place at his side. He's now seen both sides, he rejects them all, but he has definitely internalized that lesson from Snoke about cutting the ties to the past, and his interpretation of that is to smash the old ways and build his own future.
That's a huge difference from the loyal servant we saw in TFA.
With regards to Mando, I think it's too soon to tell. In its first two episodes, the show is still revealing the character to the audience, so its early to speak about actual growth to the character. I expect that will remain true for most of the first season, given that they've structured it as a slow burn so far. We'll probably learn a little more every episode about who he is before we start looking too closely at his arc.
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