I see splashed everywhere that the iPhone 5S has Console Quality Graphics. I think this is based on clips that featured extremely quick cuts. I'm not trying to be a "hater" but here's the thing, based on the numbers and power game the iPhone 5S won't and can't afford the power draw it would take to match the power hungry GPUs in consoles.
If the A6 and A5X and A7 and A8 were actually as powerful as consoles (as claimed) we would see common benchmarks such as polygon fill across devices. Even if it can support some of the same feature sets its not that impressive because the current generation of consoles is quite old, the PS4 will set a very high bar for "console graphics".
If we go with 2x graphics performance 5s/5 claim than we can say Apple can do 150million triangles per second (offscreen 1080p) vs approximately 500million triangles/s for the Xbox 360. We are getting close but the Apple pushes lots of pixels with constraints of a battery, and in the case of the PS3 the Cell does a lot of the graphical work. The GPU's in consoles also feature various special features including low level tessellation optimizations and such which isn't built into mobile GPUs.