Its really not a matter of right and wrong, so much as it is polar opposite viewpoints on how to run a wrestling company and book wrestling.
Cornette favored the much more classic approach. He valued work rate, promo cutting ability, longer matches and a focus on actual wrestling that established it almost like a real sport. Russo, on the other hand, devalued actual wrestling in favor of crash television. Matches went about 2 minutes before ending in a DQ. A lot of the guys on the roster had these crazy, outlandish and at times stereotypical bordering racist characters. While a lot of angles were considered really edgy, a lot of them were very trashy and low brow as well. In short, it went against everything that Cornette advocated. It took his vision of what wrestling should be and turned it into, what Cornette thought, was a complete joke. Cornette himself has stated many times that he and Vince McMahon as well don't see eye to eye in what they want. However, in the most famous shoot he did, Cornette said "chocolate/vanilla? Well which one is the best?" He didn't like Vince McMahon's chocolate version of wrestling, but since people have different tastes, as long as he got his vanilla, he could live with it.
I think that in Cornette's mind, the downfall of wrestling deserves to be placed on Russo's shoulders. He accuses Russo of taking a wrestling product and turning it into a cheap B movie full of tasteless garbage that will alienate a lot of the fans. He talked about, for example, the Terri Runnels miscarriage and how that might be upsetting for some people, and at what cost? Did it sell a ticket or add viewers? No, it was tasteless for the sake of tasteless. I believe he also has a big problem with, metaphorically speaking, throwing out everything including the kitchen sink on every single show to the point that now in wrestling, we feel like we've seen basically everything. Cornette has a gigantic problem with how Russo went to WCW and constantly exposed the business as being fake, and that everything was scripted. Again, Cornette is an old school guy. When in front of a camera and fans, its all 100% real, and seeing Russo go out there and do shit like "Goldberg refuses to follow the script" no doubt caused him to pop a blood vessel in his brain.
Cornette also has a big problem with Russo personally. He took extreme offense to Russo and Ferrara going to WCW and doing the whole Oklahoma thing to mock Jim Ross. Cornette respects Ross a great deal, calling him the best in the business, and also talked about how Russo tried to get JR off camera because he thought he was too southern and nobody wanted to see someone with Bell's Palsy who looked afflicted. Cornette wanted to throttle him for that. Cornette also accused Russo of being unprofessional, citing how Russo called Vince McMahon and told him he was leaving to go to WCW instead of going in to meet with him because Russo was a gutless coward.
Now, you can't argue with results. For the time, Russo had a lot of success in WWF. And there are positive aspects to Russo, like his caring about the mid card and wanting to give an identity to everyone on the roster. At the same time, you have to look at the results in WCW in 2000 and how the whole show completely bombed, which a good portion of the blame can be attributed to Russo and his laughably stupid storylines and bad decisions. Then he went to TNA. Now when TNA was just getting off the ground, Jerry Jarrett, who was helping Jeff fund TNA, said 2 things. First was "Jeff, do NOT just hire everyone from WCW." Well, Jeff did. Second, "non wrestling people trying to run a wrestling company is bound to fail." Sure enough, Jeff let Dixie Carter in and Jerry wanted to quit right there. There was a great interview Bryan Alvarez did with Jerry about 5ish years ago that I heard all of this from, so I'm not just making shit up. Anyway, the point is that Jeff hired all the goofballs from WCW, including Russo to write the show since they were buddies. Well, sure enough TNA became the new WCW, and that largely hindered them. They had great workers, the X-Division was flourishing and sadly, Vince Russo was writing the show. He was an on screen character again, we had great ideas like the big heel group Sports Entertainment Xtreme (SEX, get it? Not funny), gimmicks galore and nonsensical bullshit. And finally when Spike told Dixie to give him the boot, she secretly kept him on the payroll as a consultant, and when it got exposed (via Russo accidentally sending an email to Mike Johnson of PWInsider), Spike terminated their dealings with TNA. So essentially, Russo got TNA kicked off of network TV.
Russo with a McMahon filter worked. Unfiltered Russo didn't work. Unfortunately, we got a lot more unfiltered Russo in wrestling and it did a lot of harm, pretty much fucking over 2 major companies. At times, I think Cornette is a bit harsh on Russo, but...as I said, results don't lie.