Most of the discussion about Horizon: Zero Dawn came from people who are using PS4 Pro consoles. Everyone says the game looks great and runs well but as someone with a standard PS4 I was curious how the performance is on that platform. Luckily Digital Foundry has done a performance analysis for both systems.
http://www.eurogamer.net/articles/digitalfoundry-2017-horizon-zero-dawn-ps4-pro-performance-analysis
If you don't want to watch the video, the short version is that the game looks great and runs smoothly on both consoles. They say the biggest difference is that the PS4 renders it at a native 1080p while the PS4 Pro renders the game at 4K checkerboard.
The game is locked to 30 FPS on both consoles, which is understandable for an open world game that looks this good. Digital Foundry says it is a very consistent 30 FPS with very few dips on both consoles. The PS4 Pro version is supposed to have a patch available around launch that gives people the option of 4K rendering with a locked 30 FPS or 1080p rendering with higher framerates.