If you would like to summarize it, that would be more helpful. The conclusion will speak for itself.
First of all I would like to say that DmC DE is a good overall action game and better than 90% of games in its genre. This genre is already niche so trying to dogpile each game while propping another doesn't really help the genre much. People like DmC over DMC and that's perfectly fine of course. No one is berating another person for liking DmC.
The DMC fans just don't like being generalized by statements like "they don't like change so they are bitter" or "it's just about the white hair Dante". It's reductive discussion and uses scapegoats and strawmen as arguments. It's drive by post drivel. "Oh that one dude on youtube complained about DmC, yup must be a DMC fanboy who is bitter by the changes and hair". Just like I am sure DmC fans don't like being generalized as NT/Western dev apologists.
Now as to why the original game got its backlash, I am just going to focus on the game play changes. Stuff like character designs, art, soundtrack, writing are extremely subjective and in those categories they are just changes and hard to argue if they are changes for the worst or not (just different). I am also not going to talk about the PR failure related to the game. Game play changes are easier to quantify and compare. Here are but SOME of the changes DmC made to the original series that were perceived as worse changes:
Framerate changed from 60 FPS to 30 FPS
The series was always 60 FPS and for good reason, it was a series known for tight, responsive and fluid game play. DmC the original release on consoles didn't feature that and felt worse for it.
(They fixed this for DMC DE so now even on consoles DmC is 60 FPS)
Removal of lock on
This was another series staple and gave DMC its identity (over say stuff like GoW and Ninja Gaiden). The lock on is what gave DMC that precise feel in combat as you always attacked the enemy that you were locked on to (and it's why the Souls game have it too). The lock on also allowed the player to perform a wider base set of moves that revolved around the lock on. DmC removing lock on lowered its precision and lowered the amount of options available and they had to compensate by making core DMC moves be mapped to a separate button.
Also because core moves like Stinger were done with lock on, DmC had to make a convoluted move input which required double direction input which in these games is a big no no because it's more imprecision. Double input is objectively slower and more convoluted than a single input.
Finally removal of lock on meant that you couldn't see enemy HP bars. This was a quality of life thing.
(They added lock on in DmC DE and allowed Stinger to be used in the single direction input method. Also added HP bars on lock on)
Two buttons for Dodge
Because lock on was removed, they were left with a free button. Instead of putting in a different feature on that button, they just had it be a second dodge button which is identical to the first dodge button. This was a redundant feature and DMC games pride themselves in effecient usage of the controller.
(They replaced the 2nd dodge button with lock on in DmC)
Style system was broken, easy to exploit
Another core aspect of the DMC series was the style system. These games aren't just about killing demons, it's about doing so in style. The style bar is a mechanic built into the game for that purpose. If there isn't incentive to mix up moves then the whole battle system falls apart. DmC's original style system was easy to rank up and worst of all didn't decay below S rank even if you just stood there. This allowed players to farm points for rankings by just shooting enemies to death... very boring game play. It's like trying to play a Tony Hawk game and no matter what you do you will keep getting multipliers and never drop your tricks in the game.
(Style system was completely revamped in DmC and then they added Hardcore mode where the Style meter adhered even closer to the original series)
Difficulty neutered especially at higher difficulties
Barrier to entry for DMC games have been getter lowered over time for the starting modes but at their hardest levels they were still hard games. Without harder content, your options are meaningless if you can don't learn to use them properly. DmC on the other hand added hardly any challenge on the higher difficulties mostly because the scaling was pretty low and there were many easy to exploit mechanics in the game. Bosses were always pretty easy, mostly just damage sponge with very easy to avoid moves. Last boss was a joke if you figured out the gimmick.
(Added more difficulty modifiers in DmC to make it much harder at the top end and even starting out if you wanted. Made the final boss an actual challenge)
Easy to exploit new mechanics
There were 3-4 very easy to exploit mechanics. One was the Demon dodge system which gave you an absurd damage boost for just dodging well. Another was the Parry mechanic that allowed you to disarm enemies on a successful parry. And then there was the a Devil Trigger which was like a win button as it lifted all enemies and gave you absurd damage bonuses. Finally, you had the Arbiter Trinity Smash move aka the boss killer. If you stacked all these mechanics then you end up trivializing all content in the game. You can kill bosses in SECONDS. You can make an enemy encounter a joke by just pulling out Osiris and spinning your scythe to auto parry any attack with 0 timing. This resulted in a very tepid action game for fans of the genre.. bring out Osiris for auto parry, stack damage modifiers and just win. Worst of all the Style ranking didn't punish this playstyle but instead rewarded you even more!
(All of these exploits were nerfed in DmC DE)
Non existent gravity on moves
DMC games always had exaggerated gravity but it did have some. It's a very subtle difference that really differentiates the air combat in DMC games vs DmC. In short it just means that you can spam Rake in air DmC and never come down to the ground. In previous DMC games attacking in air slows down your fall but doesn't stop you in the air. This made air combat have a sense of urgency in the previous games and had an element of skill to them which was all but gone on DmC.
(They didn't really change this in DmC DE but moves that allowed you to go way high into the sky were nerfed)
Red/Blue color coated enemies
DMC games are about combat freedom. You are free to use whatever combat option you want to take down an enemy as long as you do it in style. Red/blur coated enemies spit in the face of that. The game forced you to use specific weapons against specific enemies and interrupted your combat flow if you tried something different. This made encounters against these types of enemies very one note and boring.
(They fixed this in DmC DE by allowing you to attack any enemy with off color weapons but they did less damage and had no hit stun. It wasn't an ideal change but it way better than before)
Most of these issues were figured out during play tests and when they released the demo. Game had more issues at the start. This is where the backlash went extreme. Thankfully the NT team fixed these issues and a lot more in DmC DE but by then it was too late, damage was done. They of course can't fix stuff like art style and writing.
As much as DmC DE fixed, there were still more issues with the game that remained but at the very least the changes made so that it ended up being a very good action game overall. However, if NT had released DmC DE as the actual game then A LOT of the backlash would've been avoided.