The PS4 has a 50% larger GPU and an easy to dev for unified memory pool of GDDR5. The Xbox One has a smaller GPU, due to 32MB of ESRAM on the APU, which helps with feeding the GPU good memory bandwidth, but is harder to dev for. The end result is that most games run at a higher resolution, higher FPS, or both on PS4.
The 2 notable exceptions to PS4's 3rd party game dominance that I can think of, are The Witcher 3 and AC Unity. AC Unity just seems like a terrible game that needed more optimization time, since Ubisoft's internal benchmarks showed the PS4 trashing the XBO in performance, and the game released as a broken POS on both systems, so I consider that irrelevant. The Witcher 3 ran at 900p on XBO and 1080p on PS4, but had slightly higher FPS in CPU limited situations on XBO. I think this was because the Xbox team made 7 Jaguar cores available to devs before the Playstation team was able. Around the same time PS4's APIs were updated to allow 7 cores, the Witcher 3 had a performance update, which put the PS4 version of the game on par with XBO on FPS. Currently both run just as smoothly, but the PS4 version is higher resolution.
The XBO has a pretty good upscaler, and it seemed like devs had an easier time with anisotropic filtering in some earlier cross platform titles. It seems like devs needed time to familiarize themselves with how AF was implemented in the PS4's SDK. Most games that suffered from poor AF on PS4 have been patched, but I think there's a few stragglers.... Like, uh, I think Evolve still needs AF patched, IIRC.
Let's see, what else? Hmm. The PS4 might have slightly better/faster hardware level decompression, so asset streaming is less likely to cause stutter and other issues. This recently showed itself on Fallout 4. The 1TB XBO has a hybrid drive, and wasn't effected by this problem.
XBO has a better WiFi chip than PS4. Not only does it support 5GHz, but it's dual band. Outright better WiFi vs PS4. If you game on WiFi out of necessity, XBO is better.
XBO supports external hard drives, and you can move data between external and internal HDDs. This makes it a LOT easier to do something like attach an unused 128GB SDD through an USB 3.0 enclosure, and get some faster load times. PS4 only allows media storage on external drives, no games, and that sucks.
XBO's internal hard drive can't be replaced without ripping the entire console apart in a way that most normal users wouldn't be capable of. I don't think Microsoft supports replacing the internal drive. PS4's internal HDD is VERY easy to replace, and Sony has instructions posted on how to do so online.
XBO's box is more roomy, and has a nice big 120mm fan over the APU. Tradeoff for this, is there's an external power brick. The PS4's APU is cooled by a 90mm fan blower design that reminds me of what you see for a lot of PC graphics cards. The smaller design allows for an internal power brick, but it can be slightly louder than the XBO's cooling solution. Both systems are unlikely to overheat given proper room for ventilation.
Then there's emulation based backwards compatibility. XBO has Xbox 360 emulation, that requires a digital download of the game, but can use the Xbox 360 game as a key. Xbox's team has generously decided that for games they port over to the emulator, that they'll allow previous owners to be able to play the games for no additional charge. Sony has started to port PS2 games to an emulator on PS4, and the ported games will have full trophy support, and some graphics improvements... but Sony's stance has been MUCH more greedy. Owners of PS2 classics from other Playstation systems, and disk based owners of the games, cannot play without buying the new PS4 port of the games.
Both systems have very large userbases, so I don't think online matchmaking should be a concern.
