The camera took some getting used to, using different lenses to take different pictures was a big deal and really influences how you think about photos. Quite a few more options too, and some old tricks like shooting portraits in Live and being able to adjust facial expressions afterwards don’t work so well because you can’t use Live with Portrait mode. But still a massive improvement.
The screen was also a big deal, Promotion and OLED and HDR content make viewing video’s a very different experience, animations are smoother. You really notice it to start with, but eventually you start taking it for granted.
The battery life is another big change. On the 7 with an old battery at 80% I could just about get through the day, on the 13 Pro I have a comfortable two days with my not-very-intense useage. Its very nice to not have to worry about recharging at the end of the day.
And the 13 Pro is significantly thicker and heavier, that also. And Face ID. And much better speakers. And a better microphone for calls.