Do you ever find that players are uncomfortable with that sort of uncertainty? I only ask because I have a couple players that do not like arbitrary shifts in difficulty for essentially identical tasks. For them, swinging on a chandelier or running up broken stairs should have a consistent DC. Of course circumstances can modify that difficulty and that's one place where 5E really shines: advantage and disadvantage are truly inspired mechanics for making rulings on the fly.In other cases, level of success may change the result. Leaping across a chasm and get a 5? You're hanging on by one hand and may still fall. Get a 10? Okay, you made it but you still have to pull yourself up as an action and so on.
In short, I think you can have both.