Watched the video w my 10 year old kid and tried to explain how impressive this is and relate it to my own experiences watching space shuttle launches.
Landing the boosters. Simultaneously. The entire live web stream, live video from space, the stats and maps, etc
Both are impressive, but spacex' achievement is making their booster truly reusable. The shuttle required way too much refurbishment to be commercially viable.
These vehicles are also completely different in their purpose so it's hard to really compare, I find them both inspiring really.
Here's a comparison made by everyday astronaut: https://youtu.be/HF69nqY3TZs
I think the best analogy I've heard for the boosters is that it's equivalent to throwing a pencil over the Empire State Building and having it land on it's eraser.
The shuttle impressive part is that they are landing the second stage, which is an order of magnitude harder than landing a booster.
The Falcon (9/heavy) impressive part is that they are flying a reusable rocket in an way that is commercially viable (which, BTW, is what the shuttle hoped to achieve).
Pretty much the whole (western) world stopped to watch it. It felt very much like returning to space for the first time since the end of the Apollo project (it wasn't, but it felt like it), it was such a step change from the previous generation of rockets. This was science fiction in action, it was going to revolutionise space travel. It even looked like a new form of transport, and the speed with which it cleared the gantry was amazing to people used to a Saturn 5.
We taped it off the TV, and I remember going back to watch it again multiple times.
Anyway, the question was, "how do they compare?". Personally, emotionally, they're pretty damn cool, but way less exciting. More so than can be hand-waved away as simply being older and more cynical.
The shuttle boosters would parachute and land in the ocean where they were retrieved and could be reused.
Back then, the thought of those boosters precisely flying themselves back to the launch site would seem like science fiction -- now it is science fact.
Just watching that video brought back memories of watching the shuttle launches -- as swish_bob says those were a BIG DEAL back then both for the engineering achievement but also culturally. It was something to admire and be proud of even if your only contribution to the project was "being born in a time and place where people do things like this".
If my memory is not playing tricks on me, when the MTV music channel started (which was also a pretty BIG DEAL in my world back then) they used animations of the shuttle (landing on the moon, I think) as part of their branding because it was hard to get any cooler than the shuttle.