We can think of things like slide to unlock but much more importantly scrolling. If something shows more the mastery of the iphone UX of that time it is definitely scrolling, who categories it as gesture now? It's completely normalized, on all other Platform of that time, you had to play with arrows and the scroll bar. Now every platform has it.
Using an iPhone felt like directly manipulating the underlying content. It was a qualitatively different experience that only superficially resembled previous touchscreen devices insofar as it used similar input hardware.
Note that Apple didn't invent the concept of a responsive UI thread with physics-based UI metaphors, for example Jeff Han demonstrated a fairly sophisticated example at TED2006[1] the year before. But to my knowledge the iPhone was the first mass-produced device with a direct manipulation interface.
[1] https://www.ted.com/talks/jeff_han_the_radical_promise_of_th...
But in the case of iOS vs Symbian:
- as others said: capacitive touch screen (this is not an OS issue, but iphone was among the firsts to use it, definitely earlier than Nokia). This is huge. Like the thing that everyone was talking about (around me) when the original iphone came out is how you could swipe to see the pictures. And it wasn't just for paging, it defined how you could interact with the phone (think pinch zooming, and rotation - not sure when these were added).
- the touch screen UI itself. Nokia played around with the touch UI before, but never really liked it. It was expressed several times internally, that touch is just a no go. But no wonder: the resistive touch screen is pretty bad, but also Symbian itself was built on the assumption that all you have is keys while iOS was built with touch UI in mind from the very beginning. (Now, of course touch was added to Symbian, but that's just not the same. Or they didn't put in the effort. Nokia even had an experimental touch phone released to the market in 2003, the 7700[1], but it was mostly ridiculous.)
- the UI just was a lot more polished, looked better, classier, the graphics was better. They had OpenGL and probably a graphics accelerator - nothing like that in Symbian, of course. (It even took the android guys by surprise, I remember reading/hearing in an interview that when they saw a demo or the release, they've realized that they had to redo the UI from scratch. Because before that they had this Blackberry-ish/Symbianish idea, they thought they were competing with that.)
- I'm pretty sure it had a better browser.
And this pretty much defines the experience, the feel a user gets from the phone. It couldn't send or receive MMS-es (some people may have used it then, but most I guess just wanted to have the feature), it couldn't receive 'push' email. I.e. you had to manually refresh your inbox, emails didn't just arrive. It didn't even have apps. Symbian had all these. It has had these for years then. It even had an app store like thing (at least you had to send in your app for verification which would then be signed by Nokia or it couldn't be installed - that was a new thing around 2004-2006, something I think nobody really did before).
I'd argue the latter, but it could be a question of framing?
But you are right that the capacitive display itself makes the interaction faster because it's enough to touch while the resistive has to be pressed. So it's probably slower and feels like you have to put in more effort.
Sure, for many, iPhones are still preferred because of the low latency, so it matters, but I suspect the iPhone would've done just as well if the latency was bad. The competition was about finger vs keys/pencil, not latency.
It would help me at least if you could specify/ list what you think were the things in UX that made it so much better than Symbian phones.