I pretty sure the CPU had nothing to do with the resolution.
Yes it does drop below it on PS4 but a 2500k at 4.2ghz is a lot more powerful than the jaguar in the consoles all things being equal the 2500k should of easily maintained 60fps.
Sometimes resolution has to do with FPS, but i have no idea how that had an effect on PS4 BF1. I think if you mean MP, its kinda hard to compare anyway, try SP on both. In BF4 i had an awful lag/stutter on siege PS4, TDM, when campining with the USAS on the top floor. On a 3550 at stock settings it didnt lag under the same circomestances, whatever that means, since online MP matches vary rather much.
PlanetSide 2 is a good test in that case, it is extremely CPU bound, about all performance is dependend on the CPU. In that game, i get as low as 20fps, or even lower, when in combat areas. I'm sure it is the CPU to fault for. My i7 920 @stock handles it much and much better (close to 60 for most), OC'd to 3.6ghz there are almost no problems regarding FPS. Ive had this CPU since late 2008.
Its a free game on both PS4 and PC. DF did some testing, they got as low as 26fps, ive had lower then that, it almost never pushes above that when in combat.
https://www.eurogamer.net/articles/digitalfoundry-2015-planetside-2-performance-analysis
Like said, those jaguars, in special @ 1.6ghz are rather slow, and for being what it is perform rather well, again for what it is. If the jaguar as in the base machines is comparable to a Q6600 in raw performance overall, less overhead and drawcalls dont lift it to much higher then that i think.
Also, wasnt DX12 supposed to help alot with the draw calls problem?
https://www.eteknix.com/dx12-can-handle-600k-draw-calls-increasing-amd-gpu-performance-600/