It's pretty much a mix of what everyone said. I have an Xbox One so I can probably speak more to that than I can a PS4, but I'll do my best to point out what you're getting from each.
Bottom line, the PS4 has better hardware, but as far as visuals go, more often than not unless you've trained your eyes to see a distinct difference between 900p and 792p then you won't be bothered because the games look practically identical. If you sit there and count the blades of grass, then sure, maybe PS4 will have 20 and Xbox will have 15, but honeslty, if you're actually playing the game then you won't see the difference. I've played on both consoles and I certainly can't tell the difference.
The big advantage I would give the PS4 is that more games run smoother, which is in my opinion the most important. There is no debate over this, it's fact. There are several multi-platform games on the PS4 that run at a smooth 60 FPS but are locked at 30 on the Xbox One. Supposedly, part of the excuse is because Kinect was using processing power, so with Kinect out of the picture Microsfot is claiming that we will see an improvement in upcoming releases, so the jury is still out on that one. Regardless, you know you're getting better specs across the board with PS4, so if that's most important to you then I would absolutely look in that direction.
Both are solid gaming rigs, but the Xbox also offers more apps for entertainment if you're into that. If it's just gaming then it works all the same because none of that stuff is manditory, it's just a nice addition if you want to partake in any of it. If this were a year ago then the clear cut choice would have been PS4, but with a new head of Xbox and a shift in focus back to gaming, the Xbox One has really starting closing that gap in terms of value for what you're getting. There's already been several UI changes and updates, all as a result of fan feedback. Either Microsoft finally realized that listening to their customers is actually pretty smart, or they were hurting in the wallet so bad that they didn't have a choice. In any event, it's a win-win for gamers because we're now getting what we actually want, not what they think we want, or what they want us to want.
Software is another major factor in making a choice. There's really no clear-cut, killer game out right now for either console that sets itself ahead of the other, so hopefully E3 will provide us with some of that. Still, it all boils down to what you like. For every Halo, Titanfall, or Gears of War, there's going to be an Uncahrted, Last of Us, or God of War. Go with what appeals more to you.
