I usually stay away from all the might-have-been-speculations, but this is something I, too pondered when I read Shawn's book.
Had Shawn left for WCW I would see every party involved lose. The WWF would lose because they could ill-afford to part ways with Shawn. If for no other reason they desperately needed someone to carry the ball until Stone Cold was good and ready.
But it's more than that. Shawn and Triple H formed DX and were a vital part in forming the Attitude Era. Eliminate DX from that time period and you pretty much got Stone Cold doing ALL the lifting by himself.
Triple H's ascend to the top would have looked very differently. Without him boldly experimenting and pushing limits in DX his career would have looked very differently. Who knows if he would have ever moved beyond being a snotty aristocrat. Would Chyna ever have come to the WWE? Could even be that Triple H would have never managed to get into the boss' daughter's panties and wouldn't that be a shame?
Then there's Shawn. Boy would he have been miserable at WCW. Yes, he'd be with his buddies Hall and Nash again. But he'd also be dealing with Hogan being the Creative Control King and Bischoff and the rest of the WCW brass not knowing what the hell they were doing. The lack of creative direction in WCW would drive Shawn insane.
Would Shawn have become WCW champion? Probably. After all he was hanging with Hall and Nash. But he'd probably also lose that belt to the Legdrop of Doom (if not the Fingerpoke of Doom) or to a 40+ year old Roddy Piper or David Arquette or someone else who couldn't wrestle a lick. Add to that WCW's tendency to keep TV matches at 4 minutes or less and you got yourself a recipe for one miserable heartbreak kid.
Shawn wouldn't have suffered his near-career-ending back injury. That's good, right? Wrong! The injury was a blessing in disguise. Shawn at that time sorely needed that 4 year sabbatical to heal physically and especially mentally. Without that forced break, he would have just gone on and on, destroying himself. And WCW, of course, would have just let him. Remember Scott Hall portraying a stumbling drunk because, well, that's what he was? Yup. That could have been Shawn, too. WCW probably would have given them their tag team titles.
And then there's Bret. Would he have left the WWF if Shawn hadn't been there. Hard to say. Fact is Vince couldn't afford to pay Bret's contract. He was pushing Bret to leave. Without shawn, though, would Vince still have done that or would Vince hang on to Bret no matter what? But let's assume Vince still needed to get rid off Bret. After all, business without HBK would be even worse. There's just no way he could afford Bret's contract.
So Bret leaves for WCW as well. I'm assuming there would be no Montreal Screwjob. Bret would drop the belt to Steve Austin or the Undertaker. Given all the information I have (Shawn's book, Bret's book, plenty of interviews and DVDs including the Bret-Shawn Greatest Rivalries DVDs) I'm guessing that if it had been anyone other than Shawn, Vince would have successfully convinced Bret to drop the belt at Survivor Series.
... And then Bret and Shawn are free to go at it again at WCW, making both their lifes and everyone else's miserable.
...
In the end WCW would go under just like it did in the real world. WCW wasn't so much crushed by the competition so much as that their product's quality simply sucked and they got canned for low ratings. WWF didn't defeat WCW, they outlasted them. WCW self-destructed and Shawn Michaels wouldn't have made any difference whatsoever, safe for perhaps a handful of nice PPV matches.
Shawn would probably have died of a drug overdose before the age of 40 or he would be where Scott Hall is right now.
Would the WWE still be here? Probably. Vince is a survivor. But it wouldn't be the same and it wouldn't have reached the heights it did.
The WWF's survival was a close enough call as it was. Take out DX (and what it meant for Triple H), and, more importantly, take out the Montreal Screwjob creating Vince McMahon the (arguably) greatest villain of all time. What's left? Stone Cold. What would Stone Cold have been without Mr. McMahon? Enough to keep the company alive, but only just.
These days we're witnessing a very mediocre product. Had Shawn left for WCW we would have been there a lot sooner.
....... At least that's my take on this.