Yea of course it should, that's why the ps4 is dominating. You mind telling me how the Xbox is different hardware wise from the the reveal besides dropping kinect like a bad habit? It's still vastly inferior on a hardware spec level.
Hardware is not the most important factor. You could have a console with 5M T-flops, but if it doesn't have any worthwhile games, or it's network sucks, or whatever, it is still going to do poorly.
The PS4 is Dominating because their rival screwed up their reputation beyond belief with the reveal of the X1 & E3. And the timing was important as it was the one time that people were actually really paying attention...and then on top of that decided that they could come out with a console priced $100 more than their competitors and people would buy it because it was better?? (which it wasn't)
And so now they are paying for that because once the stone gets rolling, it is hard to stop.....1 person get a PS4, and then his friend gets one, and then his friend gets more friends to get one. ect.
Either way, the graphical advantage the PS4 has is very small. Microsoft's problem is that the 'GAP' is much bigger in the customer's mind than in actuality.
And so your average Joe hears that "PS4 has better graphics", and in his mind, the difference is going to be quite significant.
And so he will go out and get a PS4 even if it is a few dollars more because the perceived value difference is bigger in his mind than in actuality.