Specifically, uncertainty in potential results. Swinginess. Random happenings because the dice get a mind of their own. That sort of thing.
I have played and like some "story" games, but one thing many of them lack is uncertainty. Their mechanics tend to favor participants being able to say things that become true in the fiction (even if they don't call it that).
I prefer when participants in D&D (and similar "trad" games) say what they would like to be the case, and then the dice decide how that turns out. That goes for the GM, too, btw -- the GM being subject to the same uncertainty is equally important in creating a truly surprising and novel experience.
You've been playing the wrong story games in that case

The only RPGs that are considered storygames I can think of off the top of my head that are
less uncertain than D&D are Fate and a couple of diceless games and with games like Crash Pandas the carnage is part of the point.
One of my fundamental issues with most editions of D&D is that everything is measured on a pass/fail scale with only two possible outcomes, and all spells are reliably cast rather than being mysterious and variable. The volume of a fireball is measured in cubic feet in 2e ffs. The only two D&Ds with more than a very minimal amount of potential outcomes I can think of are oD&D/1e with random encounter tables and occasional cursed artifacts, and 4e with skill challenges and ritual magic being its own thing. And failing is normally
just failing. Even worse, especially for 5e, success is frequently inconsequential; high hit points mean that each individual hit in combat is often inconsequential (and there aren't the tactics and positioning of 4e that mean you change the fiction in other ways).
Meanwhile if we look at two of the most popular modern-ish storygames (12 years old is actually pretty old for a storygame), Apocalypse World and Blades in the Dark. Both of them have as a core resolution mechanic not two but three outcomes; success, success-with-cost-or-consequences, and fail/GM's choice with a range of options. For an example of just how much more flowing and varied Apocalypse World gets than D&D here's the AW equivalent to the D&D perception skill.
READ A SITCH
When you read a charged situation, roll [2d6]+sharp [stat]. On a hit [7+], you can ask the MC questions. Whenever you act on one of the MC’s answers, take +1.
On a 10+, ask 3. On a 7–9, ask 1:
- Where’s my best escape route / way in / way past?
- Which enemy is most vulnerable to me?
- Which enemy is the biggest threat?
- What should I be on the lookout for?
- What’s my enemy’s true position?
- Who’s in control here?
On a miss, ask 1 anyway, but be prepared for the worst.
Far more variety, chaos, and uncertainty there - and as the GM even I might not know the answers before the question is asked.
To sum up my reaction to "uncertainty makes D&D better" is to think that it's like saying that vegetables make fast food better. If I wanted vegetables I wouldn't be going to the kebab shop. Which is why I was running Apocalypse World earlier tonight but running D&D on Saturday.