WWWF was renamed WWF in 1979, well before Rocky III and WrestleMania. If you're going to speak so definitively, you should do some more homework.
While I will always agree that Hogan was MUCH more important to the history of the company than Austin was, I'm not sure he is the definitive answer to this particular question.
A lot of the responses point to Hogan saving Vince's "all-in" gamble with the inaugural WrestleMania. But, Mania wasn't this going-out-of-business clearance sale where Hogan just luckily popped up and saved the day. The entire event was an investment based on Hogan's popularity. Yes, the company was apparently putting all of its eggs in that basket, but to say Hogan saved WWF is painting an inaccurate portrait of the situation.
I don't think Austin single-handedly saved WWF either. As others have said, although Austin was the biggest name of the Attitude Era, there was plenty there to pick up the slack had he been lifted out of the equation. Austin was huge, but nowhere near the level of Hogan.
However, to answer the question of the OP, I would have to say Austin prevented the company from going under more than Hogan did. Again, he was not the ONLY reason WWF turned things around in the Monday Night Wars. But, 1985 WWF was not in the pickle late 90s WWF was...so Austin is the answer by default. Hogan can't have saved a company from peril, when the whole reason the company was in any danger in the first place was this strategic investment made in Hogan. A fireman can't light a building on fire, put the fire out and then be called a hero for extinguishing it. There was no fire here until Vince decided to bet heavy on the rising star of Hulkamania. To imply that WWF was in trouble and needed WrestleMania to bail it out is misleading. WWF was fine, but Vince wasn't fine with fine. He CHOSE to go for broke and it paid off because of Hogan. But, again, to say Hogan saved this company--when he was the reason for the gamble in the first place--is incorrect.
So, disqualifying Hogan makes Austin the answer to this question.
In Bret Hart's book, he mentions the first time he met Vince McMahon.
It was at a NWA board of governors conference. Stu invited Bret to come down with him for the conference that year for a few reasons. A nice father/son trip. A good chance to show Bret off to the type of people that could help both his career, and Stu's own business. A chance to teach Bret more about the family business.
It was also the first one after Vince had purchased the WWF from his dad. This was significant because the rumblings were already out there that he didn't plan on respecting the traditional boundaries and the old promoters that made up the NWA board of governors weren't going to put up with that.
They all sat down and laid out how things weren't going to change, how New York was going to respect the traditions, what would happen otherwise. And McMahon listened to it all, then stood up and walked out of the room.
That was in 1982. Years before Wrestlemania. Back when Hulk Hogan wasn't Hulk Hogan. He was just an up and coming heel. It was still another year before Thunderlips and Rocky 3. He hadn't gone to the AWA yet to fight Bockwinkel and show how over he could get as a good guy. Hulkamania didn't exist.
And still Vince McMahon was planning his great expansion. He didn't have his foundation yet, but he was still starting to build.
McMahon was going to go for it with or without Hogan. He didn't even know a Hogan existed when he made that decision. Without Hogan? The entire thing never stands a chance and they fail.
In the 90's with Austin, I have a couple problems.
First one is that I think it's been overstated how dire the WWF's situation was before Stone Cold broke through and captured the public's conscious. We know what he told Bret Hart when he wanted to break his contract. But then very shortly after, they were still able to pay millions to Mike Tyson on what was really a massive gamble. I don't think they were in great shape, but I don't think they were as bad as they told Bret they were. That was just an excuse to get him to leave because they'd made up their minds to back Shawn Michaels over him.
The second one, is that Austin himself got the chance to break through because of Hogan and the NWO. They were the ones that got people interested in wrestling again. Before Hogan and the NWO, public interest in wrestling was at a very low point. Without Hogan reigniting that public interest, does anyone other than the die hards who never stopped watching even notice Stone Cold Steve Austin? That's actually debatable.
Sure Mike Tyson helped in this regard, but in January 1998, Mike Tyson was turning people off. He was a convicted rapist. His boxing license had been revoked. He was a side show. If casuals had already not started watching wrestling again to some degree (because of Hogan), then it's hard to say that Tyson would have been able to give Austin a big enough stage to make the same mark that he did.
This is taking absolutely nothing away from Steve Austin. He was incredible, and absolutely brought the WWF to new heights, and ushered in a new golden era for that company.
But the question who was more integral to the WWE not going under? The answer is Hulk Hogan.