Sega had so many problems, Sony's PS3 was not the only one by far. In management, SoJ held all the cards, and it was the desire of the higher ups to focus on Arcade support rather than Dreamcast support. There was a period pre-Dreamcast and during the Dreamcast's life where they decided to focus on making as many Dreamcast titles as possible.
When Sega was NOT focusing on the DC, DC sold well enough in America, but sales worldwide were generally sluggish. Sega then focusing on the Dreamcast caused massive Arcade revenue loss, which is the backbone of their company. They tumbled again. They were in a no-win situation.
Software sales were horrible, due to lack of mass-market titles outside of Crazy Taxi, NFL, RE, and Sonic. It was also helped by the massive spread of piracy, which helped Sega lose all hope for Europe (Where piracy might've helped Sonic's popularity, coincidentally).
Publishers began to quietly pull out as well and focus on the PS2 as Sega's knees began to tremble. SoA decided to invest into Sega.Net, which wasn't the wisest decision when they weren't alotted a lot of money in the first place. The Dreamcast crumbled with a bankrupt Sega. Sega wanted Software sales to take precedence on the Dreamcast, and it never really flew.
Microsoft's situation is a bit different. They have no other market, aside PC game development, to focus on. If anything, their involvement in making PC tools and games will only help their Xbox business. Their largest problem by far is getting developers with huge-name titles to take more notice of the X360. They've failed to do that with everyone but EA and SE. They have a huge blockbuster title under wraps in Halo 3, yet they have not started the least bit of Halo 3 hype, leading into their launch only being hyped by the more hardcore Madden-ites and hardcore gamers. Microsoft failed at hyping their product. They have a few more months before launch to correct this, but that's by far the biggest mis-step they had. IMO, their focus is upon getting the Xbox 360 information out there, and creating lots of buzz being the first next-generation console. They saw that as the big thing that led the PS2 to dominate, but the main reason the PS2 dominated was because we saw tech demos and all sorts of amazing games in huge franchises as much as a year before it's launch.
Their biggest advantage may be Sony's ambition. Sony's hoping on including a lot of technology for a perhaps premium price, but make it very worthwhile to the public. If Sony launches at a higher price, while Microsoft maintains a more modest one, that'd be a key advantage. I think Sony is going to go the PSP route with the PS3, adding, for the price of admission, lots of additions that push the definition of the console, like the PSP pushed the definition of a handheld. There was no media playing, web-surfing, high powered game machine video jukebox with an optical drive even in the planning before the PSP. The PS3 will apparently be a PC substitute, with the much touted ability to run new applications not strictly gaming related and it's 'home server' abilities.
Both companies are in a situation where they need the consumer to bite.
