
It seems clear that even if you hate the PS3 and loathe the PSP, it is impossible to say they are actually bad products.
Even the most hardened hater of all things Sony would really be stretching the truth if they were to say that Sony has completely failed in the areas of hand held and console hardware. In fact the PSP seems to actually be a clear winner in terms of superior equipment, but even in this area Sony cannot compete in terms of sales.
So, if it is not the hardware, then what on earth is going wrong up there at Sony?

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PSP: Two analogue controllers is what you need (Lost count of how many times I've said this, If Sony do put dual analogues on the PSP2, I'll be getting it launch day)
PS3: Just a bit too expensive. Also all that fiasco with the boomerang controlled and a crippeled online system didn't do good at launch but glad they are sorting it out. The lack of backwards compatibility is more of an issue than some people realise and thankfully, Sony had the sense to upgrade the controlled to have feedback.
But I think they'll do fine 2009/2010 onwards..
Sony are terrible at advertising.
Sony has come from nowhere and now taken 30%+ market share in the hand held console market.
Sony is making money on the PSP, you don't have to have the top console to make money for your shareholders.
Sony is having their 3rd party game roster GROW this year (4 years into its lifespan)
The PSP is going for a totally different market, they shouldn't really be compared anymore in sales.
Just like the Wii, PS3 and 360 - the PS3 and 360 shouldn't be put up to the Wii because they're not in the same market.
I'd say part of the reason is because older people won't justify the expense of buying a PSP when they already have a home console. Handheld devices are for travel mostly, or maybe for the gamer's emergency fix in case of a power outage.
The DS is geared towards kids; and parents, knowing that the DS is more kid-friendly than the PSP, will buy the DS for their kids instead of the PSP.
Obviously this isn't the sole reason, but it's definitely a factor I would guess.