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 
I rather liked it, and the more alien take on them, but I can also see why people didn't.
Part of the issue is probably that Discovery changed them too much. Previous alterations to the Klingons tended to be one thing at a time, except for the TOS films, but even they kept some things the same, like their technology.
Discovery went with a bit more of a complete overhaul, with massive changes to the language (following the pronunciation guide more closely), and alterations for both their technology, and the Klingons themselves, which might have been a bit jarring for most, especially when people were expecting more of a settled look for the TNG/TMP Klingons.
You do have the visual changes for the Klingon Empire in the Kelvin films, but that gets excused as it being part of another timeline, hence all the differences.
Things like the Klingon cleave ship, and the T'Kuvma are massive changes from what people are used to when it comes to Klingons. Klingon technology previously tended to be birds of prey that cloaked and shot energy bullets/torpedoes, not cloaked ship-breakers that used ramming speed as their main vector of attack, and Klingon supremacists didn't really exist like that. The closest we had to something like that was Worf, who was much closer to a Klingon purist/fanatic than a supremacist.
Although I personally feel that there was a missed opportunity not interspersing things with the various other Klingon designs of the time. Having a supremacist faction within the Klingon Empire, with massive visual changes (maybe due to overcompensating for Enterprise's Augment Virus?), could have been an interesting way to add depth to the Klingons, and the Empire.
Especially if that diversity of thinking between the Houses is/was one of the strengths of the Empire. Each House was more like a separate power, and they simply collaborated under the banner of the Empire.