I haven't read the whole topic so apologies in advance. Also, aologies for long post.
Honestly, the Nightcap is a strong character in the right hands and especially if there is possibility to flank the enemy team. This is not always the case in every game though.
When I started with the Nightcap it felt alright. Not too great, not too weak. The only thing that made the Nightcap unbelievably OP was the parkour upgrade. Once I started using that one, I was so fast with the character that people couldn't even come close to hitting. Seriously, I was even accused of hacking, because I could easily destroy a whole team. (not bragging, cold facts).
Before the nerf, it was my favourite character and go-to character if I needed to carry my team. Anyways, the last update took care of this issue. Parkour was nerfed and my first thoughts were well that sucks. Nightcap is so slow and not fun to play anymore. Since then, I have adjusted to the speed of Nightcap and honestly it's in a good place now. I mean in the hands of an experienced player, it is still hard to hit a Nightcap, but it's not impossible anymore.
In contrast, the Nightcap only has 75HP and no health upgrades. The class does, however, have many tricks to get out of situations.
Looking at the zombies side; the 80s is in my opinion the hard counter. 80s can easily 1-shot Nightcap and the Rocket Ride ability is broken. Moreover, you have plenty of HP as 80s to endure a battle against a Nightcap.
As others stated, Deadbeard can take care of a Nightcap in 1-shot too. Personally, I don't see Deadbeard as a hard counter, unless that person has insane accuracy. Close-range; it's hard to destroy a Nightcap.
Imo an engineer can win easily, BUT only in the event of a full stun. It takes 2-3 shots to finish a Nightcap.
Some players used Space Cadet against me, because of the auto-aim. This class CAN work, but you need to stay within a medium range. If you're too close, the auto-aim won't work. If you're too far, your shots will scatter too much.
Someone stated an Imp is a good class against a Nightcap. I think it's the same as an Engineer. If you can land the gravity grenade, then it's a free kill. I never found the Impkata a good ability. You can easily dodge this as a Nightcap. Overall, pretty decent choice.
I find the Soldier a great counter too. Decent life and damage output. Pretty agile character too. The Stink Cloud is actually an underrated ability, especially against Nightcaps.
Lastly, the Electric Slide is strong pick. Like the soldier, you have decent life and alright damage output (haven't tested since the last update). Don't use Funky Bouncer, it can mess up your accuracy. I usually get close to a Nightcap and use Disco Tornado. It's a strong AoE ability and can easily take out 50% of the Nightcaps health.
As for the other characters, I usually don't pick them against the Nightcap. Haven't tested the Wizard yet, but it's a broken character in itself which is another story! :P