The biggest thing that I have been able to figure out is that OSR will tend to shoot for the mindset of rulings over rules. Yes there is the rule book, but it's there to aid you in decision making not be the cudgle that some player can use to get their way.
In an OSR game, you only fight when you have to, because victory is not a foregone conclusion.
You might also "roll up" your character instead of creating one. Which everyone should at some point, because it's a whole part of the game that's disappeared. If you hate trying to come up with a character concept, you might well love a game where the dice can give you some ideas.
Most modern OSR games will tell you that characters have no "plot armor" and are just as vulnerable as NPC's, just like they were in the old days. But read the rules, and the PC's actually do have some plot armor after all, just a bit less.