I took the work to read trough the whole thread and i have some points I want to state:

1)All 3 consoles are comprting in the same market, theyre game machines. Some people here seems to think that while PS360 are game machines the Wii is more like a toster...I realley dont understand it, its like saying that DS and PSP are not competing, cos PSP is a powerhouse and DS is focused in casuals...It doesnt make any sense.

2)I also noticed some people seems to consider N games, such as SMG, as "casual" WTF¿?
Mario, as well as allmost all Nintendo big historical franchises is 100% hardcore, it can be a little less "masculine" than Halo or Gears of War, but it is still core gaming. There are different kind of games, thats all.
Give a Mario game to the lil Timmy and I can assure you that he wont know what the hell to do. And not even start with Zelda or Metroid...

3)Everything crazzyman says makes absolutely no sense. I even think he make such statements just to have fun.
I cant believe how hes still waiting for the PS3 to rose, like waiting for the Mesiah.
Seriously man, stop worryng about the sales and enjoy your PS3, is a great machine, but I really doubt it can duplicate the greatness of the PS2...stop waiting for that to happen.
Why do you think that MGS will make PS3 resurge, when GT4 didnt?
Also, why do you put so much confidence in FFXIII?
It will make PS3 big in Japan? It may be, but I can assure Squenix is probably not to happy with the PS3 2 millions userbase in there...

Are people buying wii's instead of PS3's or 360's? Yes, therefore they are competing

The percentage of players owning more than 1 console is higher this gen than during the previous gen...

Not everyone that has a Wii is going to buy another console but the number of cross consoles owner will be significant by the end of this gen ( I would guess 10% or more of the Wii owners).

Just look at the people posting on this site, far more own several consoles this gen than they did last gen.... 

http://www.gamasutra.com/php-bin/news_index.php?story=18107

Finally, NPD says only three percent of respondents said they owned two of the three next-gen consoles, and only 2 percent said they owned all three.

Wii is competing with 360 and PS3. One more Wii sale = one less PS3 or 360 sale. People generally buy only one console per generation. 5% buy two or more consoles. 2% buy all three consoles of a generation.

Okay, to put it simple:

If a developer has to decide which console he is going to support with games and he makes a Wii game instead of an Xbox 360 / PS3 game... are the consoles competing or not?

Louie, I think a lot of people fail to see that side of the equation.

While the market can sustain 2 console directions, the development community cannot magically support both just as equally. Especially with the explosion in cost for art assets. Publishers are having to make tougher resource allocation decisions than they ever have before and if the consoles are competing behind the scenes for publisher attention, they are directly competing...simple as that.

The Wii is competing, casual or not. It has hardcore games, even if they aren't chock full of guns and violence. I guess hardcore could be defined by learning curve, but that's a whole other topic.

As for Final Fantasy XIII, I question how much of an impact it will cause to PS3 Hardware sales in Japan. FF12 sold 2.4 million in Japan, with the PS3 at a user base of 90 million. Then, PS2 was the dominant console. The market is at a different place now and PS3 won't have half the Japanese userbase the PS2 did when FF12 was out. With a smaller userbase, it would be harder for it to sell as much. The game will be awesome no doubt, but if GTA4 didn't boost HW sales in EU/US, I doubt FFXIII alone will boost sales in a fickle Japan.

 NES/SNES/GEN/TG16/N64/etc aren't traditional?

@NJ5 nice find, I didn't realize so few people owned multiple consoles.

I'm not sure if I commented already but err someone already hit the nail on the head when they said a Wii sold
is a PS360 not sold in 93% of the cases.

Ahh but the marketing is where it's being askewed a bit, take a step back and look at the 3 relations.

Business model + marketing = competition, as long as your trying to sell something your competing with someone else in this day and age. So if the Wii isn't competing with PS360 then who is it competing with? Refrigerators? Well it sure isn't Barbie dolls as both are marketed heavily towards females.

Let's take another look at what Nintendo is claiming, I'm sure we have all heard "we are not directly competing..." - Iwata (I slaped his name on it as he's said that dozens of times, so I feel pretty safe doing that.) A business model is a set of guide lines that a venture is based around, it affects everything from the products to the marketing strategy to even the logo of a business, as such a business model set's in stone the nature of that business by aligning it's methods and executions with it's expectations in the most favorable fashion.

The idea is that a succesful business model becomes traditional once it's accepted by competitors - hence the term traditional being transposed on to gaming as the directional assests of the products (software and hardware) are copies of the business model. (See EA) The idea of franchises are just successful products under a business model.

The Wii is different as it's widely accepted that Nintendo is exercising a disruptive business model, which if they become successful it will probably become the new traditional model. (People like making money, I know it's wierd.) Does that mean Nintendo is competing... yes and no, they aim to upheave the old business model but as far as users go they are aiming for what traditional business models claimed and what their new model claims.

"It's just good business."

Buuut, as far as install bases go, Nintendo has appealed already to who they need to, they just need to keep the reminder there. Now they will probably be pushing even harder into the install bases of the PS360, they probably aren't doing this, for lack of a better term; actively. It was more part of their business model and just the natural progression of their product.

So I guess the final answer is to the question: Is Nintendo competing directly? Eventually.