Refresh rate doesn't affect the in-game FPS. With 60Hz monitor you just won't be able to see more than 60 FPS on your screen or you may get screen tearing in some cases.

Keep in mind that 1080 being so new, the graphic drivers are not yet fully optimized either.

However, for ESO in most cases, the CPU's processing power is the main FPS boost, followed by HDD/SDD and RAM. I can run the game on Ultra@1080p with an ease using 970m (which is a laptop GPU) and still get over 70-80 FPS in most places and dungeons. Now when I go to Cyrodiil for an example, the FPS drops considerably and not because of the amount of graphics my GPU has to render, but because of the poor optimization of calculating people's paths, trajectories and the mechanics involved in general. That's mainly a CPU issue. It's easy to test what's your main bottleneck, just Google some monitoring tools.

I'm not living a stationary life currently, so I am unable to test out a desktop rig with the new 1080, but from what I've heard from friends, it's a bit waste of money, considering how much cheaper the 1070 is and 99.9% of the time it will not be the GPU that bottlenecks you, whether it is 1070 or 1080.

TL;DR I'd get the 1070 and upgrade to a more advanced edition of 1080 in the future when it's actually needed. If you want to stream or record, just get a dedicated streaming card instead of splurging money for 1080 or even worse, SLI, which is so hindered by the beta drivers that it's just worthless when you take a look at the benchmarks.

Also, to give an idea of how crappy ESO is to test or evaluate any hardware then; Even when you are using the world's fastest consumer grade SSD + ultra-low latency DDR4 (the new 950 Pro with up to 2.2Gb/s speeds and HyperX 2400hz CL13) as I am currently in my laptop, you will still not be able to load zones quicker than with for an example Evo 850 and you can still experience weirdly looooong loading times in Cyrodiil for example.