For me, the quality that changed the most was the character of James Kirk.
In both films nuKirk has been shown to be:
*Better than everyone else.
*A man of action (act first, ask later).
*Prone to mistake due to lapses in judgment caused by ego and hubris.
All three of those define ShatKirk.
The only difference is nuKirk's immaturity. He's younger and never had a father figure. He was also thrust from Hicksville townie to Starship commander rather rapidly.
The reason why this part of both films' themes is because it's an on-going character arc.
What's the problem?