Forget all this 1080/720 screen resolution nonsense as most console gamers sit so far back from the TV they can't tell what resolution the game is running. That said, I wonder how many gamers out there on PS4s and Xbox Ones even bother try changing their screen resolution on their TV or console from default 720, I bet not many if their TV doesn't do it automatically.
PS3 was more powerful than the 360 but I don't remember reading 'oh the Xbox 360 is underpowered compared to the PS3'. Multiplatform games on either of them were the same, give or take a few. Which was down to developers bad programming, not hardware limitions. E.g. Bayonetta and Oblivion on the PS3.
On paper the Xbox One looks less powerful but it is on par with the PS4 because of the AMD architecture they are built on. Many developers have said this many times, especially Indi developers. Funny many major gaming websites don't mention this and you only get the full story from technical research or gaming podcasts.
Okay, first of all resolution is noticeable, 720 vs 1080p is crazy obvious on y 50" screen somewhere like 2.5metres from the screen, VERY obvious. Ps4 will be far more likely to hit 60fps and stick there with the smallest amount of variation while a game designed to not drop much below 60fps on a PS4 level of hardware will likely maintain a lower fps rate and drop/vary frame rate far more significantly on the XO. higher fps and small variance = better experience.
There are differences now in games that aren't particularly optimised for the latest consoles, not in all games and often the difference is small. Console exclusives WILL show up the 50% shader advantage the PS4 has. There is more fundamental power, they will make games to use that power, this hasn't happened yet and won't happen realistically for another 6-12 months but will continue to improve over the next couple years after that. That is the same with every new generation of consoles.
Power wise, the 360/ps3 were pretty close in GPU power, they certainly weren't far enough away from each other that dev's targeted different level of effects and quality. The difference between ps4/XO is massive compared to the difference between the 360/ps3.
360 was the lead platform, it was easier to code for and out earlier. The Ps3 was complex to code for(mostly the CPU) and while the CPU was a pain to extract performance out of, once dev's did get to grips with it there wasn't also extra untapped GPU performance. By the time the PS3 was the "preferred" platform for dev's it was so late that it didn't matter, and there wasn't 50% more shader power to take advantage of a better cpu.
This gen Xbox is both more complex to code for, has worse tools and is significantly, massively slower on the GPU side. This means the PS4 is the lead platform, it's easier to code for, has better tools and at no stage will the XO make up this raw power difference. At best it can overcome the tools disadvantage and become less of a pain, it will never become better and will stay miles behind till the next gen. As more games target the PS4 in power level, there will be bigger differences in games, not smaller.
That there are differences now when most games are being re-released for the new consoles, or even new games whose main target is still the 360/PS3, is impressive and ominous. As more games come out purely for the next gen systems, and more exclusives come out, it's almost certain that the gaps will be bigger, the PS4 will be the "better" option in the majority of games.
The simple fact is, why buy the worse console, even if it's only every third game that runs at a higher frame rate or better resolution, why actively buy the worse console, that costs more, even the good deals lately have really just put it on par price wise, and those deals have gone. £350 for a kinectless XO or £350 for a faster PS4... at £250 a kinectless XO or £300 for a Kinect including XO is good competition, but same price why buy the console that has worse frame rate and resolution in enough games to make it clear which is more powerful.