From wikipedia: 

In the video game industry, AAA (pronounced "triple A") is a classification term used for games with the highest development budgets and levels of promotion.^[1][2][3][4] A title considered to be AAA is therefore expected to be a high quality game and to be among the year's bestsellers.

Given that definition, the PS4's AAA exclusives would be The Order and Bloodborne. For the X1 it would be Halo, Tomb Raider and maybe Forza. 

No offense but i was asking you as a gamer, in what way a AAA game benefits you more, according to this definition ?  if you are a gamer and not a shareholder, that's pretty damn not smart to consider more a game because it's a bestseller and because it is highly promoted with high budget ( especially if most of the budget is used in promotion...). And that doesnt answer the other questoin : There is no way you can know a game's budget ( and where is the limit between a AAA game and an other ? 1M? 2M ? 3M ?), it's just a guess unless it's officially revealed, you can make a good guess for a small game , but in most cases, there is no way to know that for a retail game, there are much more things than graphics to consider like developement time,  all the work on content.

A gamer shouldnt care about a game being AAA or not, according to this definition, a game can be a high quality game, with good budget and wouldnt be considered as a AAA still just because it's not highly promoted and doenst sell more than 1M? like Persona 5 ( will be the best game of the year very likely, just like P4G was), it will be in top 3 of most ambitious games in term of content and quality this year, the only difference between this game and your AAA games is that there is not next gen graphics, just decent graphics with a big focus on the quality of the product before the marketing.

Bloodbourne and Bastion are currently two PS4 AAA exclusives that are out this year so far.  You can't claim a game is AAA until it releases...

So, should games that work on the xbox one through backwards compatibility be included in this list?

Sure. We can add those 18 games :)

Should we add the 350+ games playable on PS4 through PS Now as well?

Are you missing some titles?

http://blog.us.playstation.com/2015/06/21/the-drop-new-playstation-games-for-6232015/

To be fair, the majority of retail games fit that discription even if they are a new IP or not particularly big in the states. The number of examples that you given should be much higher. 

No. That doesn't fit my agenda bro. We ain't including them.

Seriously though with joking aside, Only reason I'd include the xbox one games coming through backwards compatibility is because you can actually buy them on the xbox one and own them forever and don't need to pay for xbox live gold or anything else to do that. Plus there are subtle differences, some better and some worse over what was on the 360 and work is being done to improve the individual games. Not as much as would be in a remaster but still some work. I don't see much of a difference from the games coming with backwards compatibility over games like Ultra street fighter which is on this list, other than the fact that Ultra street fighter has a disc. Games such as Bastion or Ultra Street fighter could come to xbox one through backwards compatibility and run just as well as the ps4 version but would they still be thought of as exclusive to the ps4 as this list suggests?

Plus should Halo: ODST be included on this list? It had a full on remaster and isn't present. I'm genuinely curious as to what should be on the list and what should not and I didn't mention PS now because it works completely different to backwards compatibility on the xbox one and is completely different to ports such as Ultra Street fighter as these games can be bought and are not streamed and reliant on an internet connection to play which is limited to a 720p output.

It actually was a genuine question as I agree with you that it's impossible to draw a line.

Should we count all the flash games playable on PS4 and Xbox One as well? XD

It's impossible to satisfy everyone.

Narrowed down to games that actually matter:

PS4

The Order: 1886
Bloodborne
MLB 15: The Show
Axiom Verge
Helldivers
God of War III Remastered
Until Dawn
Everybody's Gone to the Rapture
Uncharted: The Nathan Drake Collection

Xbox One

IDARB
Ori and the Blind Forest
Massive Chalice
Rare Replay
Gears of War: Ultimate Edition
Forza Motorsport 6
Halo 5: Guardians
Rise of the Tomb Raider