To clarify...
1. Every generation Microsoft claims the same, except this one where the lines are blurred because you can't, so instead you guys have gone around the bush way of dealing with it, by misinforming or fluffing with cloud figures ranging from 40x the performance and discussing transistor counts (5 billion!) instead of actual specs, like the former even matters. That and eluding to things that you've neither explained nor can be proven.
2. The PS3 was not strictly more powerful than the 360. The 360 had the better GPU (which Microsoft themselves championed), the PS3 the far better CPU. The 360 also enjoyed unified ram and more ram at that. The situation is not at all the same this time around. The PS4 has better raw performance, unified ram and more ram bandwidth (with respect to the main bulk of DDR3 vs GDDR5). According to some developers it also has more mature dev tools and better customisations. Then there's the OS footprint, which this time around is purported to be smaller on the PS4.
3. You talk about DirectX and API's, but you have to realise, low level coding and working beyond the constraints of said API's is what has given Sony the ability to lead the charge on graphics and tech with first party games this generation. With the PS3 notably, where despite the GPU deficit, the most technically and graphically proficient games were on the PS3. And where on the PS2, despite a massive hardware disadvantage to the Xbox, the PS2 still had games that could compete (such as GOW2, GT4 etc).
In other words, sometimes such API's actually hold developers back instead of the opposite, which thankfully Microsoft is somewhat understanding this time around which is why you're allowing lower level access on the Xbox One.
In other words, I don't know if the Direct X API thing is one that effectively champions your point.