That is very possible. It was a long time ago. All I remember is you had two camps and one had The Rock and Stone Cold Steve Austin and the other side had Booker T.
It's an easy mistake to make because one side of the invasion was represented by WWF wrestlers and the other side was represented by WWF wrestlers.
Yeah WWF's main stars were Stone Cold, The Rock, Undertaker, Mankind, Triple H, Kane, Kurt Angle, Shawn Michaels, etc. while WCW had Hulk Hogan, Scott Hall, Kevin Nash, Sting, Ric Flair, Goldberg, Booker T, DDP, Scott Steiner, etc. There were some notable transitions during the Attitude Era, particularly when Paul Wight (The Giant/Big Show), Chris Jericho, Chris Benoit and Eddie Guerrero went from WCW to WWF.
What I find shocking is that the "WCW Invasion" angle didn't have Hogan, Nash, Hall, Goldberg, Sting, Flair, Steiner or Bischoff, like come on that's like almost all the most important people in WCW.
As for the product itself, WCW was mainly known for having the larger talent pool, especially when it came to cruiserweights, but was criticized for having relying on the older, more-established wrestlers for the main feuds. On the other hand WWF had a more limited roster which made the undercard less noteworthy match-wise which they made up for by giving everyone storylines and gimmicks. The more limited roster, especially with so many top guys going to WCW, also forced them to build up newer stars which helped them in the longer run.
Personally, I was too young to really enjoy the Monday Night Wars but I'm definitely much more familiar with the WWF storylines, matches and wrestlers of that period than I am WCW, especially since I'm more of a fan of the over-the-top storylines and gimmicks. Russo and Ferrara did notably switch to WCW and kind of had that style there for a big but obviously it didn't work as well as it had in the WWF.