The difference being that Nintendo was dominant in prior gens to the 32-bit era. If history shows you anything, it's that the losing team never dictates how the industry moves and exits hardware when all else has failed. Fortunately, Xbox is backed by Microsoft, so it may never meet that sort of fate, but it will also never enjoy the sort of success that has only befallen Nintendo and PlayStation — the two undeniably biggest brands in gaming by many, many miles!
Nintendo was one switch away from being gone themselves. Had they launched a another traditional weak console it too would have failed badly.
Yes MS has deep pockets, and that's why things are drastically different than a Sega or any other company that failed.
Also you have to define failed. MS has supported it's OS as the gaming platform for PC gaming, it's largely succeeded in this regard, and it helps them sell the OS which doesn't show on the xbox books.
They are coming off a generation selling 50 million units. That's not what the leader sold obviously, but it's also not 10 million and shut it down. It was obviously big enough to greenlight this generation.
You also have to know that if MS didn't release PC versions of it's games, it's console sales in the last two generations would have been higher.
The xbox brand still has value, and they have a deep array of studios going forward for thier bread and butter (Selling OS and software for it) regardless of the console side.