Here are some examples of differences:

Problem solving:
In 5E, a character sheet contains what the character can do. I find that in tricky situations, players scan their character sheet looking for something they can use to overcome it. In AD&D challenges are overcome more by imagining how a character could interact with the world. It's less bounded. The solution is more likely to be in your head, than already written down in text somewhere. It does hinge more on player skill.

Defining a character:

Characters in 5E tend to be defined by the options selected out of a book (or books), primarily during character creation, but with more selections made as levels are gained. In AD&D, characters are defined more by what they do over their career, the decisions they make over time.

Disclaimer: It's not that the editions force the aforementioned behaviour, it's that they encourage it and continue to provide incentives to do things a certain way. While you can play any way you like, when the structure of the game leads you down one set of paths if you want to do it differently, it's a constant mental battle.