The PS4 is able to run games well due to the fact that it uses GNM and GNMX, with the shader language being PSSL. Basically, it is much lower level than DirectX 11 and even DX12. Additionally, the developers only need to target one single set of hardware as they know that if it runs at a set level then it’s pretty much guaranteed to run the same on every other machine. Unreal Engine 4 uses modern rendering techniques that are more akin to realistic physically-based rendering pipelines.
You can’t really find comparable hardware for the PS3 as it has a massively powerful custom IBM CPU that does a lot of the processing for the system, even taking over the GPU. Think of it as something GPGPU does for the CPU, except in reverse. Compression algorithms and coding allows developers to stretch a lot of potential out of the PS3’s hardware, which is how it can run very good looking games with only 256mb RAM allocated for games and the rest for the OS. The PS4 relies on GPGPU for CPU-based processing and its GPU is equivalent to an R7 260X, however with its heterogenous architecture it is able to have a 5GB VRAM buffer for game assets with the rest going to the OS. Additionally, the PS4 shares the same sort of compute tech that the R9 290X has (asynchronous compute units) which helps with GPU rendering and GPGPU.