The 360 would actually win for me if Banjo Threeie had been made instead of Nuts and Bolts and they had another action adventure game.

It does pale in comparison to the PS3 and Xbox 360 however. As great as the PS2 was it was a product of its time really. With first person shooters and WRPGs now some of the most popular genres it may not have had the appeal it does today. Even with the PS4, it's most popular games are shooters (Battlefield 4, Killzone 4, Call of Duty series, Destiny, etc. etc.).

This... Nintendo have tons of variety and im not just talking their own game franchises ,which cover multiple genres. Games like Wonderful 101, Madworld, Bayonetta 2, Zombi U etc all help diversify a gaming library.

While I agree with you that those 3 games are loaded with quality (objectively speaking probably the best in their genres for 7th gen) but PS3 had those genres covered with strong entries as well. FPS (Killzone 2), JRPG (Ni no Kuni, Persona 5 will probably end up as PS3's best JRPG though) and racer (Gran Turismo). 3 games don't make a highly varied library alone.

And what about the best survival horror (The Last of Us), best stealth (Metal Gear Solid 4), best tactical RPG (Valkyria Chronicles), best platformer between PS3 and 360 at least (Ratchet & Clank Future), best hack and slash (God of War 3), best action-adventure (Uncharted 2), best puzzle-platformer between PS3 and 360 at least (LittleBigPlanet), best action RPG (Demon's Souls), etc?

Point is the PS3 has quality strong entries in literally every genre and that's what makes a varied library in my eyes.

Yep. PS3 has easy the most diversity ! Quality in every genre, the best Console I have ever owned. Now let's see what PS4 will offer, and already offering ;)

FPS, third person shooter and open world games like GTA.

Didn't knew SNES had fps, tps games.

However, when you entertain the idea that the market has changed, you also have to entertain that the games the PS2 would have seen would have also adopted to that market. I think the games market is much less broad than it used to be, that's why I don't think we'll really come close to the variety we used to get on the older consoles.

Ever Sony said they wanted the PS4 to try and get back to the diversity that the PS1 had. They even acknowledged themselves that the PS3 lineup is a lot less diverse than their previous systems.

Yes the PS3 might have more examples of FPS, WRPG and TPS games etc. But the PS2 has them, and also has a lot of styles of game well covered beyond that, which the PS3 missed entirely. There was far more variety in genres like racing, shooters, 3d platformers etc. and a hell of a lot more quirky off shoot gaming concepts. The PS3 played it so safe in comparison to the point of boredom as far as innovation and experimentation went. This however is completely understandable when you factor in how much development costs ballooned with the requirements of HD gaming. Indie gaming is starting to make these game types viable again, but it is the 8th gen where Indie gaming will truly shine.

It just quite simply is nowhere near as broad a software offering as the previous PlayStations.

You mustn't have played DOOM, Wolfenstein 3D or Jurassic Park then XD

Did the PS3 have any decent Theme Park and City Building simulations?

I'd say that the PS2 has the most diverse library of all consoles, but the PS3 it's certainly up there!