Three big points to me that make combat seem to pop much more:
-The sound engineering is, compared to Dark Souls, way better. The deflections have weight and therefore are distinct from blocks just on the sounds alone. But all the other sound are just richer and deeper than a lot of Dark Souls SFX.
-There's a graphical fidelity to things in Sekiro that you only really saw in environments and gear in Dark Souls. Animations are generally much better, most importantly the guy you'll be staring at the whole game, their animations match the awesomeness that before was just lavished specific enemies in Dark Souls. Effects in this game, the ones that it has, actually look like AAA visual effects versus what has always seemed a little quaint and amateurish in Dark Souls, even Dark Souls 3.
-Everything is just faster. Of course the rapid deflects and your own attacks, but also your dodge animation. The way you snap in to Deathblows right after a deflect instead of Dark Soul's slowly drawn out synch kills. The rate of your R1s in Sekiro is he closest thing to the pace of Dark Souls, which you immediately out pace as your block or dodge interrupt, use a combat art, use a tool, or get in to deflect, which breaks you out of your slow R1 combo. Again, it's like instead of reserving all the crazy cool shit for their enemies, in Sekiro they give you the kind of speed and badassery you wished you'd have in Dark Souls, but instead settled for precision and judgment and timing.
Sekiro has kind of reminded me that loving Dark Souls so much basically made me accept a lot of its faults, and even begin to sing their praises in some ways. Like accepting the plodding, methodical and largely stodgy combat. Sekiro feels more dynamic and action-y in the way you expect modern AAA games to be....but brings From Soft's brand of storytelling and art and thoughtfulness around the action. It's a more mainstream-feeling game where I don't feel like anything has really be lost over what they've done before. It's not so fundamentally different from Dark Souls that you can't immediately recognize familiar and comforting parallels. But it's different enough to feel fresh and worth exploring like you're a newb all over again in their fucked up worlds.