If MS is to have any chance of matching Sony even in the US, they are going to have to push harder than they have ever before.
During the PS2 Era, the Xbox was late and expensive and the fight was basically done, so Xbox was just trying to break in. It wasn't really competing.
During the PS3 Era, the Xbox had a year lead, a price advantage, and a library advantage, as well as a multiplat advantage for the first half of its life. This is when it started competing with PS.
Now, during the PS4 Era, the Xbox has lost most if not all of its advantages from the previous gen, and its competitor has gained the price and multiplat advantage. Thus, not only must it overcome all of these challenges, but it also must defeat the same competitor, it tied with despite having many advantages (without its advantages)

The PS4 probably will not have the market dominance that the PS2 had, but the Xbox is definitely going against an opponent who is much more prepared this time around, and still distinctly remember losing in the past.

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I doubt the relevance of fall off because this can be attributed to next-gen adoption. Especially, since 360 faced no competiton from its successor in its eigth year, while the ps3 had to compete with the PS4 and XONE in its holiday season of its eighth year. They both had to compete with the Wii U but I doubt how much of an effect Wii U sales would have on 360, especially when it was more expensive last year.

All in all it seems rather circumstansial.

Last gen and this gen are hardly similar, at least in terms of launches and early post launch sales which are the only metric we have right now

Again, its circumstansial. I'm going off you're chart so I don't know how much the PS2 sold during the 360's launch but I doubt it was close to its peak years. 

The generations are very chronistic.

But it is a fact that the PS3 and 360 are on different timescales and that the competition that the PS3 faced in its eigth year was much heavier than what the 360 faced, and even what the ps2 faced in the same timeperiod.

Comparing the PS3's eighth year to the 360's ninth year is more accurate because thats in the same timeframe, with the same events happening to both of them at the same time. With that consideration your own chart seems to go against your claim that "The ps3 is dying quicker than the 360 actually."

However, this decline is also accelerated by next-gen adoption, so I don't understand how this information has any bearing on predicting the future success of the next gen consoles, expecially when we don't know how 9th gen will look.

Some users think it has no chance of making 2nd place let alone first.

I on the other hand think it's still too early to call.

It will come down to MS's stubbornness to bundle kinect.
The longer they keep it bundled, the slimmer its chances become.
I bet if there wasnt kinect and they were the same price, sales would be very close. Even the resolution thing wouldnt have mattered as much as it does because of the fact that you can play the better version of multiplatforms while paying less*.

*Excluding cases where retailers have charged ridiculous prices or forced people to buy 3 games in a bundle because of PS4 shortages.

That is the PS4!

Not saying that the ps3 is a failure, it just didnt live up to the PS2's dominance.

I just do not think the One being 400$ would change things that much or get anybody to buy the One who would not have but what it would do is get 360 fans who intend on getting a One at one point or another to go ahead and get it now instead of down the road

Always third place, you gotta admire the consistency.

Also, whole year less on the market people, you can pretend it doesn't matter, and pretend that a lot of people didn't buy the competition rather than go without a new console, but it doesn't make it any less of a major factor.

Yep, in fact Ballmer asked twice to nuke it again, but the first time Bush Jr almost choked on his pretzels, the second, Obama was more open to the idea, but after conferring with Michelle and Hillary, he came back disconsolate, opening his arms and told him: "Sorry, we can't".