When comparing PS2 to PS3, you should remember that PS2 had supply issues. Unlike PS3.
You can of course compare launch numbers between any console, but for every console situatiation is diffent. PS2 propably gained from Dreamcasts early launh. People were still waiting for what the generations consoles have to offer. Dreamcast was really no diffent from PS2 (DC only had online play), but Nintendos powerhouse was yet to come. Until Microsoft announced Xbox, the new powerhouse.
Both of them was too far away to wait and since DC and PS2 had already showed what will be seen in 6th gen, M$ and Nintendo could not offer anything really new (6th gen= 4 exactly the same consoles). Sony had the brand and 3rd parties and Sega hadnt enough fanboys to keep up.
And PSX, it was new and unproven. Did not bring anything new for gaming, but it was marketed in clever way.
Sega was first in market, but release of 32X for Megadrive just before Saturn launch, made fanboys angry and buy the PSX. Nintendo was too far behind, but it had something new to offer. Until competitors copied it. Expensive development costs and expensive media made 3rd parties turn to Sony and Sega and finally games for PSX were 20% cheaper than N64 games.
Now PS3 does not benefit from the early launch (unlike PSX and PS2), Sony brand has taken damage from its rootkit (the rootkit was there, because most of the people doest even know, what rootkit is), PlayStation brand took damage from PS2s, which many of them broke, Nintendo gained some brand with DS and the PSPs success compared to DS, will not help this fifth PS to succeed either.
Now, compared to GC, PS3 has few disadvantages if the 3rd party is leaving (which it looks like at the moment), GC had strong 1st party support (of course Sony pressed the panic button, by announcing that it will expand its 1st party, but this is going to take about 2 yrs) and the price, when Nintendo pressed the panic button, it lowered GCs price massively. Sony cant do this for PS3 being so expensive to manufacture.
Compared Wii to PS3, you can either buy PS3 with no games or Wii with 6 games (Wii sports not counted) for the same amount of money. If you buy a console for gaming, which will you choose? Nintendo will also have a free online, unlike Sony (well Sony has free for 1st party, but not the 3rd party if they want to charge you). Nintedo also has Virtual Console where you can find hits beyond 20 years, which Sonys and M$s services cant compete. And Wii offers you something new, unlike 360 and PS3.
And for the 360? M$ does not have a line for their console, they are trying to compete with Sony about what you can do with the console and forget (just like Sony) all the gamers, but 360 is much more cheaper (a players choise from those 2).