I don't think they ever found one, and I think that's ok. The mascots are holdovers from the Nintendo-Sega era, when games were mostly played by people under 25, and the graphics made it impossible to create anything but cartoonish characters.
When Sony came on the scene, they tried to make due with Crash and Spyro, but both felt too "LOOK AT OUR MASCOT! SEE OUR MASCOT!" to work, their games were of questionable quality, and, of course, neither character would end up being Sony exclusive.
As gamers got older, the need to address diverse tastes mattered more than a mascot, and that is where Sony benefited. Some might argue that Jak & Dexter or Ratchet & Clank are the mascots, but there are too many Sony owners who never played either. GTA, GT, and FF didn't use recurring characters, and now 2 of those are no longer Sony exclusive. But doesn't much matter as it was always the broad array of games, rather than just one title, that made Sony a success.
The question then is why does MS have Master Chief? I suspect that is largely an accident. HALO turned out to be the one good, must have, exclusive title for the XBox. Nothing else came close. That sort of made MC the default "spokesavatar" for the 360. If the XBox180 had as diverse an array of other titles that sold just as well as HALO, odds are good that MC would not have become as important in marketing the system.
ADDENDUM:
And remember, it took years for Mario to become a mascot. He'd been around, largely unnoticed, since Donkey Kong, but it was SMB that made him a star, and made people run out and buy Nintendo systems. Sega realized that the only way to challenge Nintendo at that time was to challenge Mario's supremecy, and they built a whole ad campaign around Sonic being cooler than Mario (he wasn't, but I digress). And that battle - Mario vs Sonic - became a proxy for three generations of console wars. It personalized the fight at a time when people still thought that the market would only support one console. By the time Sony arrived, we all knew the market could support multiple consoles and Sega was in the middle of commiting suicide. The edge was largely gone. And besides, we like our rivalries to be clearly defined. Once Mario vs Sonic was established, there simply wasn't room for another. Adding Crash to the mix was like trying to add the Devil Rays to the Yankess-Red Sox rivalry.
