The difference in this case was that Microsoft didn't NEED to get off to a rock solid start. They launched the 360 into a void, there was no competition. They didn't have enough stock, the launc lineup was mediocre, and the Xbox 360 didn't exactly fly out of the gate. The reason why this isn't remarked on is because it wasn't a problem, the 360 had time to build up a sizeable user base, and they managed 6 million by the time the PS3 came out. Not an incredibly large amount, but not exactly meager.
Meanwhile, the PS3 launched one year later than the Xbox360. It is not enough to simply follow the curve of the Xbox for it. Imagine you're a publisher, about to finance a game. You have to project what the user base of the consoles are going to be like a year down the track when your game is released. Since the PS3 released, it hasn't gained ground on the Xbox, it's actually lost ground. Over a year has passed and the Xbox360 has actually extended its lead over the PS3. As a game publisher, you'll look at that, you'll look at the software sales of the Xbox360 and compare it to the software sales of the PS3, and the decision isn't difficult. In one year, the Xbox360 is most likely to have the larger install base, and you're most likely to make more money off it (especially if you're a western publisher). Conclusion, either make an Xbox360 exclusive, or multi platform but put the most resources into the Xbox version.
Of course, this means the Xbox is likely to see more games, and as such, more customers, feeding the circle. And the longer the PS3 loses ground on the Xbox360, the less likely it looks like overtaking the Xbox360, and the less publishers are going to decide to release exclusives for the PS3.
If the second console is to win, it needs a strong launch followed by prolonged periods of brisk sales. Even if it takes 2 years to overtake the leading console, publishers will look at the future, see that this console is going to overtake, and start backing it. But if your console flounders out of the gate, and loses ground on the competition, like the PS3 has, then you're going to lose developer support, and lose the games, and lose the customers.