Sony actually struck gold with the Mortal Kombat 3 deal. It wasn't even a good port (the fucking load times), but closer to the arcade than 16-bit. It was a 2D game, but MK3 was with the 16 bit crowd the most anticipated fighter. I believe it was the best selling 32-bit game of 1995 in Europe. It was the game that managed to migrate SNES and MD users. The most faithful version was only on PSX.
After this, Sega locked UMK3 for themselves on 32-bit, which is the superior version of MK3. But by then the hype was down. I think UMK3 barely did anything despite the game being way better. MK3 was also getting old by this time.
But I think the worse 3D did contribute to its failure. These 2 systems were compared side by side, they were also displayed in stores side by side. If you run both Daytona and RR its apparent that RR looked more appealing. Factor in the higher price tag Saturn had and it was an easy choice for consumers. I think this is how it went. Ofcourse, not having much software that would attract Genesis owners didn't help matters too. Worse, Sega didn't keep their word about this sytem. They would support it and see it as an important pillar, but by early 1996 the Genesis was pretty much done for. I still had one and while SNES went on (partially because of the N64 delay), there was almost nothing to look forward to. 32-bit systems were unaffordable for youngsters over here (being 400-500 euros each when they launched, when converted) I knew many who actually bought a cheap SNES (which was priced at 100 or less) with DKC2, Killer instinct et al.
Rayman was also riding the success that year especially in parts of Europe. While it was also on the Saturn, it was 2 months late in US and 1 month late in Europe. Sega in both Europe and US contrary to popular belief was trying to push 3D much harder early on than what people think they did. The problem was that they didn't have games that would get players to leave the Genesis, the PS1 had those. For the games they both had either the Saturn got late, or Sega never bothered to grab and Sony would eventually grab those games later.
UMK3 was a get but we are talking a few months gap between the release of UMK3 and MKT. MKT sold truckloads on the PS1, and was well marketed by Nintendo as a mature game you could get during the early days of the N64. UMK3 wasn't pulling anyone by then.
Worse 3D may have contributed to the Saturn not being able to salvage a profitable niche, but even if the 3D was the same as the PS1 I don't see any path away from failure a year after launch outside of Japan. The system systematically died everywhere in the west around the same time. Price tag is probably the only early factor that may have helped them a certain amount, but when you have the same games lineup, the same developers you are ignoring or letting your competitor grab, the same strategy that doesn't work to bring those Genesis players to your new product, and Sega already by end of 1995 laying the groundwork to port games to PC, expand beyond their consoles, funding various pet projects, then I can't honestly say anything would actually change.
Fall the next year, BEFORE Tomb Raider came out. Saturn was already selling peanuts and the PlayStation was way ahead, and in Japan was already widening the gap quickly for several months leading up to that same point. Sega did not have the time to have messed up for as long as they did. Saturn wasn't the only system that ended up taking the fall from that failure, the Genesis did too. Sega released some high-production genesis games but they weren't selling like the SNES later releases. I think people forget that Sega didn't have a war chest to make all these mistakes and afford to quickly reverse them, or if they chose the wrong path forward to easily be able to spend their way to a different lane. They were spending almost as much as they were bringing in or more since 1992 between arcades, consoles, development teams, and other projects. They were putting a lot of hope and dependence on the Model-3 thinking that machine would cause people to become so engaged that those games would make Sega bank coin after coin for years and it didn't go anywhere. Saturn not being able to capture even 1/5th of the Genesis footprint in the west was the other knockout to their finances.