I wouldn't have changed a match; I would have had Shane McMahon buy out WCW and continue running WCW as a separate company in competition with his father. The "McMahon Family Problems" of the invasion angle would have been MUCH more interesting if say, Stephanie was to stay loyal to Vince, but HHH jumped ship to WCW in support of what Shane was doing. There would be no WCW wrestlers on WWE programming unless it was a major acquisition that from either brand. Imagine what would have happened if when Kurt's contract was up, he jumped to WCW rather than TNA. Christian moved from a WWE midcarder to a WCW main eventer.
The guys like Styles, Daniels, etc would have ended up in a place where the titles (such as the X Division) could be traced back to the likes of Rey, Guerrero, Jericho and other "top stars" of the WWE with the Cruiser division. The whole aspect of the "TNA vs. WWE" debate would be totally different if the WCW was still its own separate entity with the massive history behind it. Plus, as big of a crowd favorite as Shane was for those who followed WWE, I think the audience split would be enough to carry the creativity of which McMahon could out do the other.
I don't think of it as a "continue the Monday Night Wars / Attitude Era" type aspect, but rather a "imagine how good the programming could be to this day" if WWE kept along with their "superstars" campaign and WCW carried the torch of "wrestling" the way TNA is trying to do these days. Like WCW or not, the heritage it had behind the titles made them very valuable, whereas when they came into the WWE they have done nothing but decrease since the E Universe took over. Just a thought.