I think the difference is 'badassness' in 4e didn't come from easily passing DCs. The math was largely irrelevant to that. It came from the DM building more and more amazing fiction around the DCs, and from everything else. You might hit a Balor about the same way you'd hit an Orc at the appropriate levels, but FIGHTING a Balor is WAY different. It has an aura, resistances, and powers that have a number of varied effects. The PCs at that level also can do things like get really screwed up by a bunch of effects and then just shake them all off, or fall dead and stand right up again, etc. Even at Paragon you find that your characters really are a LOT more potent in absolute narrative terms than they are at lower levels.
So what I found was that the mechanics 'fall away'. The game becomes highly narratively focused, or at least focused on what the PCs want to DO, and not really on numbers. I think there were definitely some flaws. The SC system didn't quite work right until the RC version, and the build process was too focused on making the numbers. However, it worked.
Now, I can see, since your game apparently was so focused on tactical skirmishes that nobody even took non-combat utility powers or feats, then it became a one-dimensional game. That's too bad, but the other dimensions of the system DO exist, and they're really powerful.
I don't think there's anything horribly wrong with the way 5e does things, it just focuses much more on numbers. Everything seems to be about whether or not you can get the hard DC. I don't think the story in our game is bad, but mostly I just miss the way in the 4e game we could pull crazy stuff that I wouldn't dare to even try now.