I want to say both. In our game, most rules, like combat (5e btw) and skills, are by the book. however, i do encourage my players to try and think outside the box. I do not allow them to roll a million times when building until they have like all 18s and 20s at level one (in fact one guy got mad at me for this) and I do make sure they know there is always more than one option. they can choose to fight it out or they can choose to run like hell. It is always up to them but you know that does change the game. so it depends on what they want to do but everything, not just some things, have different outcomes. action and reaction. so i am sorry, but that quiz needs a third option
It's a bit unspecific. I'd say take the best of both worlds: old school has more depth to it, but modern-style games have less tedium and tend to be more streamlined. For most purposes, I'm in favor of a GM-led simulation approach. And yes, that means players should be allowed to fail. However, I think even failure should be made entertaining, and there should be clear feedback beforehand about their chances.
No more: "You see a portal, no telling where it goes." - "I'll go in and find out." - "Well, it beams you into the sun, you're dead. Whoops."