It seems as though you like to keep your hardware for a long time, before you upgrade, like most of us. Going with 8 cores as opposed to 4 cores seems a lot more future proof. 8 cores may not be really necessary right now, but in 2 or 3 years you might be a lot better off with more cores. Also, The performance difference between a 8350 and a 1600 is huge. I'm sure it will play ESO just fine. If you do decide to go with the 1600, get the fastest memory you can to go with it. 3000 or 3200 DDR4 memory is recommended. I'm sure whatever you decide to go with, will be a vast improvement over what you have now.
P.S. FPS drops in ESO are just a fact of life, whatever your hardware is.