It would be a totally different ballgame, pushes that did happen would not have happened... You cannot say he would have feuded with Austin, because if Hogan hadn't gone to WCW then Steve Austin may never have left there and other WWE pushes didn't happen as a result.
Bret beats Hogan at Summerslam after winning the KOTR and Hogan starts to get boos, at the same time he comes across the path of Shawn Michaels and Diesel who are starting to get face pops and he uses them to soften up Bret for a win and the title back at Survivor Series, turning him full blown heel by taking out Bret and Shawn... this pisses off Diesel who goes face and feuds with Hogan through to the Rumble, which Diesel has to win to get his match. Shawn and Bret get in each other's way, costing them their shot and they begin to feud with each other, with Owen Hart in Bret's corner.
At Wrestlemania X Diesel defeats Hogan for the World title and Bret and Shawn face off in the first Ladder Match for the IC title - Owen costs Bret the title and Randy Savage makes the save for Bret.
Meanwhile in WCW - Rick Rude misses the trip to Japan that ended his career as he is being offered a top run by Vince and clandestinely makes the switch while Vince releases several talents such as Charles Wright, Crush and Jacques Rougeau who go straight into WCW. Wright and Adams form a new tag team and immediately win the straps while Jacques Rougeau enters the upper mid-card title, skating dangerously close to being sued over the Mountie gimmick, he wears the same outfit and keeps the same character, just using his real name and becomes part of the Dangerous Alliance. He feuds with several younger talents over the TV title and later the US. In the Main Event - Vader feuds with a newly returned Scott Steiner over the WCW Title - Rick is in the US title picture with Steve Austin.
Rude makes his debut at Wrestlemania X feuding Mr. Perfect, costing him he and Tatanka's match to Money Inc. DiBiase tries to pay Rude but only succeeds in getting a Rude Awakening for his troubles, setting Rude as a lone wolf. At RAW he states he is out to decimate the roster, one by one until he gets what was rightfully his, the WWF title - he also singles out Hulk Hogan for a barb about how he refused to face him in the past for the title and how even Warriors were scared of this real man. Bobby Heenan offers his services to Rude once more and he too is given a "Rude Awakening" that "ends his career". Rude beats Perfect to win the King Of The Ring title, after Perfect had dedicated his win to Heenan when The Brain tries to help and appears hurt.
Meanwhile, at KOTR 1994 - The Undertaker battles Yokozuna in a Casket Match and Owen & Shawn face Randy Savage and Bret in tag team competition with the caveat that whoever gains the pinfall becomes #1 contender to Diesel - Randy Savage takes advantage of a quick opportunity to pin Owen and gets that role - Bret is frustrated but happy for his friend.
In their title rematch, held inside a cage and with Jesse Ventura as special referee - Diesel beats Hogan, when he gets in Ventura's face and their old feud backfires, Jesse slams the door onto Hogan's head to stop him escaping.
Savage runs down and is torn, he is a good guy but concerned about his friend Hogan, who is bleeding profusely. He is quickly blindsided by Rick Rude who attacks him with the sceptre and "puts him on the shelf". On RAW he reveals that he has been named the #1 contender to Diesel's title for Summerslam, by virtue of his KOTR win and Savage's inability to compete due to "severe concussion".
This is just how 1993 and 1994 could have differed, lots of different knock on effects. You can see here that Rude would be heading the route Austin did, within 2 years he could easily have been in that "face/anti-hero" role that Austin was, had simple decisions been different - How someone like Shawn and Bret would have worked higher up the card, but still not have been the "main guys" while big men like Hogan and Diesel were around and marketable, how some lower guys could have stepped over to WCW like Scott Steiner and gotten bigger pushes. That kind of story would have prevented the "sucky" era of 95 in WWE and the boom in WCW that got them to the stage they could poach talent. Eventually Hogan would have moved, probably Savage too - but certainly had things been done this way, Bret, Shawn, Diesel and Rick Rude would have all been major players by the time Hogan and Savage did depart - Where it left the Undertaker? that is the question - I could see him being the "odd man out" in that WWF and being the "shock switch" in the way Luger was.
almost all of this is some of the most ridiculous 'what could have been' shit I have ever read. Hogan would never had let someone of lesser size beat him in a match, let alone a feud. Bret and HBK would not have been brought to main event singles stars, HBK stays at upper midcard IC level, with maybe a token title shot or two. Bret lingers in tag teams, and also feuding with HBK. Without HBK being higher on the card and with more influence, Nash likely doesn't go far, though Sid might stick around and do similar to what happens, except with feuds against Hogan and possibly Warrior instead of HBK. Lesser power for Nash and HBK also makes lesser impact for Hall.
The Attitude era might be delayed as prior to the full effect, they were moving into the Faction Era, where every one was part of a four or five man group. Delay the Attitude Era and you don't get Stone Cold, Rock, or Mankind, which lowers the legacy and impact of Taker, HHH, and Vince himself. Vince likely doesn't acknowledge on air his backstage role with the same rippling effect.
Rude still goes when he did to wcw. Perfect as well since he's in the same role, never going to win the big title as long as hogan is around. Savage also leaves as the real issues between him, Vince, and hogan are too much to stick around and deal with. Remember, he wasn't wrestling and vince had made it clear that he didn't want macho man as a wrestler any more, only as a commentator. if he stays, he likely doesn't step foot in a ring for a long time. Eventually Hall and Nash leave, and likely bring HBK instead of Hogan. With HBK and the rest of the Klique in wcw, there is no DX, so no New Age Outlaws, no HHH, just Hunter Hearst Helmsley. That is, if he didn't stick around in wcw. Perhaps instead of nwo, there would have been some version of a wcw DX.
And Austin leaving wcw would still have happened. He would still have gone to ecw, and likely come to wwe, but unlikely to make the same impact since there would have been little chance of the same situations happening that lead to the creation of 'Stone Cold'. Same can be said for Foley. Delay the timing slightly and the beats that lead to their popularity are off and they don't quite hit the highs that they did.
Without DX and Austin to feud with, then the Rock likely doesn't become the story he has been. With Hogan still around, you can be sure the Rock doesn't get the opportunity for the movies he did, and that shortens the spread of wwe popularity.
If Hogan stayed and Savage and HBK go, then the 'outsider' and nwo would be completely different. A heel HBK turn would not be as unexpected as a Hogan turn, and neither would a Savage turn, since both had by that point spent considerable time in both roles of face/heel with success.
Not to say it couldn't have succeeded, but it would have been different. And that could have meant the difference between the short overtaking of wwe that wcw had, or a longer/slower drawn out fall of the company. Perhaps the AOL/Time Warner buyout doesn't happen or happens earlier/later.
the biggest effect though could have been on the Hart Family. Perhaps with HBK gone, and Bret on a lower slot on the card, he isn't signed to that 20year contract that Vince later tries to dump. This would mean no Montreal Screwjob and bad blood between the mcmahons and harts. Bret could still have left to try his hand at getting a higher spot with wcw without the drama of the events leading to the screwjob.
With no resentment towards the hart family on the part of mcmahon, perhaps owen doesn't pull that dumb spot and break austin's neck, which took years of austin's career. With no stress of the so-called betrayal by bret and the injury to austin, owen might not have been put in the position to do that idiotic stunt that lead to his death. Bret might have had the chance to work with Goldberg more safely, if he managed to get to the level he did, and might not have suffered the concussion that ended his career and the strokes it caused that nearly killed him.