I am the kind of person who enjoys "big weird" scifi like Stanisław Lem. Stories about trying to relate to and find common ground with something so alien that the prospect of even understanding is basically hopeless. Star Trek usually doesn't do stories that, which makes sense as it often uses alien races as allegories or stand-ins for real-world human relations.
That said- I thought those early Klingons were super weird and scary because they were just so alien. It really made sense thinking about how it took a century before they could get to the events of Star Trek VI, and it made the Khittomer accords feel like so much more of an accomplishment. Like- you made a treaty with WHAT?
And just aesthetically their ships and armor looked like something out of HP Lovecraft or HR Geiger:
This is not to say I dislike how Klingons were portrayed previously, kinda like Mongols in TOS or Vikings in DS9, just that they never felt scary to me. They never felt like warriors. I was never afraid for the gallant crew of the Enterprise D (a science and exploration vessel) going into battle against Klingons. But I really enjoyed the alien-ness Disco tried to go with. Anyone else with me?
EDIT: PEOPLE I SAID WHO'S WITH ME NOT WHO ISN'T CM'ON 
Most of this reasoning is irrelevant to me simply because I don't view each show as seperate. I watch DIS s1 and see this Klingons and can't help but think "so what about Kang, Kor, or Koloth? How do they look right now?"
It doesn't matter how cool or scary these new klingons look, they have four nostrils and elongated heads when before they were more like buff humans with ridges. That's irreconcilable to me, regardless of how the actual aesthetic makes me feel when I watch an episode.
Taking it at face value, the Klingons looked like TNG, then they lost ridges, then regained them with even more than we'd ever seen before, then they lose them, then they go back to TNG? That's annoying.
Like Klingons.