Does higher VRAM mean better fps?

Solution
No, many other factors at play.

Always use game benchmarks to compare performance, not the specifications of the card. For example the 1060 3gb and 1060 6gb are actually different gpus, the additional performance of the 6gb comes more from the additional cuda cores, than the extra 3gb of ram.

Vram is more to allow you to enjoy higher resolutions (and detail settings) without the vram getting full - when vram gets full performance tanks due to having to use slower system ram.

This was quite a brief answer, and doesnt cover it all.
No, many other factors at play.

Always use game benchmarks to compare performance, not the specifications of the card. For example the 1060 3gb and 1060 6gb are actually different gpus, the additional performance of the 6gb comes more from the additional cuda cores, than the extra 3gb of ram.

Vram is more to allow you to enjoy higher resolutions (and detail settings) without the vram getting full - when vram gets full performance tanks due to having to use slower system ram.

This was quite a brief answer, and doesnt cover it all.
 
Solution