1060-3 and 970-4 are basically the same thing. There will be games where the 970 makes better use of the extra 1Gb of vram, and gets 1-10 higher fps, just as there's games that make use of the 1060-3's ability and gets higher fps by 1-10.
The only real difference is power, the 970 is a Maxwell gpu and really requires 500-550w psu, the 1060 is Pascal and needs only 400-450w. So depending on the psu available, the 1060-3 might be the better choice, even if slightly more expensive, as you may not need to upgrade the psu, or if the 970 is cheaper and your psu is good enough, that might be the better option.
The 970 has a full 4Gb of useful vram. It has 3.5Gb of high speed vram and 0.5Gb of slower vram, that's only used if required. But...