If just compare the GPU only, of course PS4 is stronger, there is no doubt on this matter. If we just compare the max GPU raw processing power, it's 50% more than XB1.
However, the overall performance difference is not that much. Also, it has weaker CPU, that means the GPU has less object to handle (which actually helps to get higher resolution / FPS).
If we use GTA V as an example. There will be more cars / people allowed to display on the screen on XB1, but PS4 can gives out better graphics. So, it's down to the users' preference. Someone prefer a bit better graphic (TBH, it's just a bit better, I own both console. And for most of the games, there is no way to tell the difference if not putting the display side by side). Or prefer more moving objects (which may makes ours brain believe there is more details).
The spec of course is important, if there is no real world demo yet. But now, a buyer can simply go to any game store, look at the real output, and then pick the console they want. So, no need to purely rely on the spec anymore.
In general, we tends to believe more moving objects means more details. That's just how our brains work. So, unless there is really a huge difference in graphics, better GPU but weaker CPU not necessary looking better at the end (in terms of what we feel). Interestingly, quite a few of my friends owns both consoles. And most of them "remind" me to buy the XB1 version (if the same game avail on PS4) not because of playing together on live, but they feel that XB1 offer better graphics (from their own eyes and brains, but not the spec). They are the practical gamers, not academic / professional gamers. Most of us play games on high end PC as well, we know what's real good graphics.
It may be easier to understand if we put this to extreme. e.g. System one's GPU can offer 1080P 60FPS, but CPU is extremely weak that can only handle 10 squares. Which means we can see 10 high resolution squares in 1080P on the screen, that's it. On the other system, the GPU is 50% weaker, can only offer 720P 60FPS / 1080P 30FPS, but the CPU is 20% better, can handle 12 squares at the same time. So that we can see 12 squares on the screen now, but lower graphic setting. Which one looks stronger? The 2nd system, because most likely our eyes can't tell if the square is in 720P or 1080P, but our brains tell us straight away that more square means more details.
Of course, this may be over simplified, but that's how we "feel" at the end. Once again, a normal people shouldn't able to tell if the screen is powering by a PS4 / XB1. And no way to tell that PS4 offer 50% better graphic by our naked eyes. I did try very hard to compare both output (for the same game), and found out it's meaningless because the overall gaming experience is so close (in terms of graphics, but not including Live, controller, etc.)
Now, DX12 games are coming to XB1, which will further reduce the overall graphic performance difference (software plays a very important part in overall performance). Will it even make XB1's graphic looks better? I don't know, but I don't think so. I tends to believe that will only make us even harder to tell the overall difference between PS4 and XB1.
As the others suggest, for personal gaming, choose the console base on the games availability. If you want to play with friends, then get the console they have. If still no decision, I personally will suggest XB1 because it's much quieter under full load, the PS4 like a little jet engine in comparison (I hate fan noise).
