To answer this question, let me take you back. Imagine if you will, that we are back in 1994 again, your 10 maybe 11 years old and you've been watching wrestling your entire short life. I want you to look through those eyes. When you see Hulk Hogan suddenly working for WCW it made you think maybe this WCW show is worth watching more. This is the guy you've been watching since you can remember, he's Hulk Hogan, the biggest star in history, Hulkamania is running wild in WCW. You see him on the other show and you have to wonder what is so great about WCW that Hulk Hogan wants to be apart of it. It was a big deal, he WAS the WWF and there weren't any real replacements for him when he left there either. Sure, people we refer to now as legends were there, but they weren't legends then. They were all guys working their way up.
The WWF at the time was home. It was what you watched. WCW was around and you may have watched it from time to time, but the WWF was where it was at. When Hogan was officially with WCW it told you there was another dog in the yard. The only thing though is that as mentioned by some earlier, Hogan was not as big a deal technically when he went to WCW. He did have some baggage and his name had been tarnished. As a kid you probably didn't know that, but you knew by 1994 that Hogan had lost some of the luster. In a lot of ways Hogan going to WCW helped him as much as it did WCW itself. It revived his career which had slumped pretty bad basically since 1992. For that reason and that reason alone I have to say that Hogan going to WCW was not the biggest moment. Keep in mind, when he made his move there was no Monday Night War ensuing either. It was big, but it wasn't THE moment.
The WWF by 95-96 had changed completely. It was the "Next Generation" as they put it. The WWF wasn't as strong as it had once been, and WCW was picking up steam by this point. They had Hogan, Flair, Sting, The Giant, and Mach while the WWE had Shawn, Bret, Taker, Diesel, and Razor. As a kid WWF was still the top dog at the time, even though we know now they were having some trouble, THEN they were still the biggest and the best. WCW even with the talent they had, wasn't really a threat. Sure, they were making good with what they had, but it wasn't enough yet to really take it to the WWF. Even when Luger showed up in surprising fashion on Nitro, that really wasn't as big a deal either, at least as far as how it affected the Monday night situation. WWF wasn't really losing anything when he left. Sure, they had invested a bunch of time and money in him, but he wasn't anywhere near as successful as they had tried to make him, and they knew he wasn't going much further anyways.
Then one Monday Night, your watching both shows going back and forth because now you can, and you can see people you like on 2 wrestling shows. Your on Nitro right now but you are waiting for a commercial to end before you switch back to WWF. Suddenly you notice a commotion in the crowd, something is going on but you can't make out what. You see someone going through the audience but can't quite make out who it is right off hand. Then in a matter of seconds you see the figure and realize that for some odd reason Razor Ramon is on Nitro!!!! You had just seen him on WWF not too long ago, so this doesn't make sense to you. Why would a WWF guy be there??? Then he gets in the ring, and utters those famous words " Hey Yo! You all know who I am, But you don't know why I'm here." WCW from that point on was red hot.
Once Razor Ramon went to WCW and he and Diesel started The Outsiders everything else including he NWO with Hogan became possible, and without his surprise attack on WCW it wouldn't have been as big a deal either. It didn't hurt that he was easily one of the most popular stars in WWF. See, WCW's problem before then was that they had plenty of real big talent, but they were all older guys. They didn't have any YOUNG talent, even sting was older talent to the company. No one wants to watch their grandfathers fighting on television. So, when they got Razor who was hugely over in WWF that made a really big statement. The smartest thing they did that whole time too was playing it off like he was still with the WWF and it was a takeover. It might not be the actual start of the Monday Night Wars, but it was certainly the point that sent everything to it's heights.
There are plenty of other moments that were important and played their roles. But, this one I think tops them all. It shouldn't be either Razor or Diesel though, they should have been put together for the poll, and in that case it was their arrivals in WCW that really make everything else happen. It was Razor and Diesel who convinced Hogan to do the heel turn and the NWO thing, and it was they who made people watch WCW because it was so cool to see WWF guys running a muck in another company. It just made the WWF look bigger in my opinion. It established that WWF was the bigger better company, because it was their superstars invading the WCW.
If they had tried a takeover angle with their own guys it wouldn't have worked. They needed bigger stars than they already had and they found the exactly right people for the job. When Razor Ramon showed up on WCW everything changed from there. I would argue that without the departure of Razor and Diesel from WWF you wouldn't have got Stone Cold, DX, The Rock, or Mankind. They were made out of necessity because the WWF had once again lost some really big talent and needed new guys. Also, they needed not just new talent but new gimmicks because of how dramatically Razor and Diesel changed things once they got to WCW. They were the ones who really made "Bad" cool. WWF had no choice but to follow in suit and come up with some edgier, harder hitting, more serious programming to compete which led to the birth of the above mentioned characters. In essence you could say that one moment was the one that set it all off to the next level ushering in a new era in professional wrestling, that led us to where we are now.