I definitely agree that there was a rivalry between WCW and WWE fans, especially when one promotion was routinely putting on the better show.
For example, in 96', after Hogan's turn, WCW definitely had a lot of momentum (and, to be sure, much of this started as early as that first Nitro) and were the hot brand. I had tickets to that year's SummerSlam and while I remember a pretty good crowd, among my fellow pubescent wrestling-addicted friends, this was pretty uncool. I remember talking up the finish of the Boiler Room Brawl match and several of my friends rolling their eyes at how the biggest storyline in WWE was a manager turning heel on a "tired gimmick wrestler." Compare that to the "Is this real or fake?" buzz of the early nWo and its not hard to pick out which one was going to seem "cool" to a bunch of 13 year olds who considered themselves "smart" because they were on RSPW, joined e-feds, and taped ECW in the wee AM hours.
In 99', the opposite was true. My "WCW friends" tried desperately to convince the rest of the gang that WWE sucked, but, at that point, the nWo was really stale and the WWE was crushing them in ratings. The rivalry continued until WCW closed and my "WCW friends" moved onto what was left of ECW and Japan/Mexico tapes.
Another thought - I've always viewed one of the key differences between WWF and WCW was that WWF has, dating back decades, always run with a clear, top babyface in the prime spot, while NWA/WCW often put more focus on a heel. This may have also played into the "Hogan hate" of 95' and pre-nWo 96' as a sizeable portion of the audience had grown to feel comfortable cheering the heel (which explains the popularity of guys like Sid, but also of certain guys like Terry Funk who didn't play by the rules often).
Could it be that WCW fans catered to a more cynical, "well-read" crowd (and that these cynical fans were willing to give a glance at unknown wrestlers because of their indy reps) than WWE fans, who were "less educated" but dependable for cheering the guys they intended to promote?
