This topic deserves a lot more credit than people here have given it.
There were many theories before the release of both consoles, that they are mimicking the patterns of their handheld cousins - and there hasn't been much to discredit these theories yet:
PSP / PS3
- more expensive, premium solutions
- aimed more at hardcore gamers, young male demographic
- "hit" driven software sales (big hits sell well, other titles not so well)
- pushing their own non-standard disc format
- favour graphics over input innovation
- software sales struggling (relative to other machines)
DS / Wii
- cheaper solution
- more casual, family orientated titles
- better "across the board" sales (cheaper, simpler titles tend to sell ok - MySims, Carnival, etc)
- not aimed at pushing new "tech standards" on to consumers
- weaker graphics, innovation in input ("fun")
- strong software sales
...
The main advantage the PS3 has over the PSP (and its a big one) is this: the PSP aims at being a portable console, around PS1/PS2 tech power. Not that many "original" games are created for the platform, and many of the ones that are - are eventually ported to the PS2 (etc...).
The PS3 is the "top" of the gaming chain - it will have more original, exclusive titles - and games that haven't been seen before, and can't be easily ported down.
The main disadvantage the PS3 has over the PSP - extra competition. Whereas there are only two handhelds - the PS3 is also competing against the 360, PC & PS2 devices.
...
In conclusion - I wouldn't be at all surprised to see the same "patterns" continue in the future. The PSP hardware is selling well - and the PS3 hardware will also sell well.
However, the DS is killing the PSP in hardware sales terms - and I expect the Wii to do the same to the PS3 (which it already is) at least in the foreseeable future.
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More important will be software performance. To date, the PS3 has significantly underperformed in terms of software sales - the Wii has done pretty well, and actually created some hit new franchises (with sales hits - WiiSports, MarioParty8, WiiFit being some obvious ones that come to mind).
To date in Japan: The Wii has sold 11m software units, and the PS3 around 3m - no pack-ins, and both released around the same time.
Worldwide - this site has 11 1m+ sellers for the Wii, and just 2 for the PS3 - both of which were launch titles, and heavily included as "pack-ins" in various bundles over the last year.
The PSP has 11 1m+ sellers - and the DS has 35. Similar ratios to their console brothers.