Two sides of the same story here. On the one side, ex-Xbox man Peter Moore, who explains how the decision to include a HDD in the original Xbox eventually led to its early demise (they even had a pre-determined kill figure!), and thus why they didn't bother making them standard in the 360:
...not having a hard drive in every Xbox 360 was a hard decision, but we wanted to get price under control. The hard drive in every Xbox killed us; we we're still selling it at $199 and the hard drive was like $70. That's why we prematurely left the original Xbox, because the more we were selling - there was still great demand - it was killing us, and there was no way to bring the price down. So in the end we determined at around the 25 million unit mark that we just needed to slow this thing down and just not sell any more, and move to the 360 as quickly as we possibly could. And to this day people still believe we left the Xbox too early but it was purely for financial purposes.
So that's the Xbox. But what about the PS3?
SCE Worldwide boss Shuhei Yoshida says exactly the opposite. That the 360's HDD plan is silly, and that including a HDD has been an integral part of Sony's strategy with the PS3:
It's one of the things we really supported when the hardware specification was decided for PS3. Like Microsoft did, we could have had an optional hard drive and settled for cheaper combinations of hardware, but if we had done that - from a [development]standpoint - we cannot rely on every consumer to have a hard drive.
So that really helps us to focus on [the fact that]every consumer has a hard drive. Now we can cache data so that gameplay is seamless.
Truth be told, the HDD was the best thing about the original Xbox, and the 360 is only going to increasingly suffer from the fact developers can't build games that require a HDD. We kinda wish they'd just stuck with it, since the cost argument is surely nullified by the fact nobody buys a HDD-less Arcade.