The original nWo angle was not a collaborative effort by both companies. It was Bischoff raiding WWF talent out from under Vince McMahon. The nWo was Bischoff's version of the WWF. It was his way of pitting WWF vs WCW without using the initials. He had gotten the idea from Japan. I would find it hard to believe that Vince would just send his stars over to another company, so that they could create the biggest angle ever and send him to near bankruptcy.
Though, to this day, there are some who still feel that Survivor Series 97 was a work, a scripted event. The evidence they give is that from the incident, Vince became a heel and used his character to propel the WWF back to the top. Bret could have been in on it, since it was a way for him to leave the company as a hero, and not with the "sellout" label that was put on him. It's an interesting theory, but with the way those two are today, I doubt the incident was scripted. Though some, even some wrestlers like Lance Storm, still think it's a work.
I honestly do not think the WWF owned WCW back in early 2000. For one thing, not even the notion of that has been expressed by any of the people in the industry, not the promoters, not the writers, not the wrestlers, and especially not even the journalists, who report the slightest notion of anything, accurate or not. The stuff that happened in 2000 was just a complete mess. Vince Russo's WCW was in complete disarray with injuries to Bret Hart and Jeff Jarrett. The plan he had been working on since his arrival in October 99 was in pieces. Without the two main wreslers in his Souled Out ppv in January, he was forced to throw things together. As a shocking twist, he planned on having Tank Abbott win the World title. When Kevin Sullivan and co. got word of this, they convinced Bill Busch, who originally brought in Russo to replace Bischoff, that Russo was crazy and to remove him from power. The wrestlers objected to that and that's why the Radicalz left. After realizing that Kevin Sullivan was putting WCW down the toilet, WCW officials agreed to bring in Vince Russo and Eric Bischoff together in hopes that a joint effort by the two would send the company back up. But Vince Russo's controversial ways, especially the Bash at the Beach incident with Hulk Hogan, drove Bischoff away after a few months. Russo received more and more criticism as the weeks passed and after receiving a concussion, he quit and left WCW in even further chaos. Terry Taylor and Johnny Ace tried to mend WCW but it was simply too weak and Time Warner wanted it gone. The WWF really had nothing to do with it, it was the hierarchy of the company and the backstage politics that brought WCW down that year. If you remember, the 2nd to last Nitro occured under the impression that Eric Bischoff and Fusient had bought the company. Bischoff came on the show to announce the next week would be the "season finale" of Nitro. With Nitro off the air, he planned on spending the time after on securing a television deal and working on way to fix the mess that WCW was in. But days later. the Fusient deal fell through and the WWF took the chance to buy WCW, they quickly reworked the final Nitro, incorporating it into the current Shane vs. Vince storyline.
There is no Undisputed Champion anymore. It's split into the two titles that Jericho won at Vengeance last year. I think it was done to add more separation to the two shows. Eventually, I think the two shows will become completely separate promotions. There's also a lot of evidence for WWE Raw gradually turning into WCW Nitro. Notice the new position of the announce team, the return of the WCW title belt, and of course, Eric Bischoff "in charge". I think the WWE wants another crack at WWF vs. WCW. This time, they probably hope to do it slowly and right, unlike the mess that it was last time.