Mini vs Full Size GTX 1080 Inquiry

The underlying GPU and memory structures are exactly the same - just the size of the circuit board and cooling solution is changed.
It will still have the same number of CUDA cores, etc. and base and turbo clock speeds won't vary too much, so performance should be very similar, depending upon the effectiveness of the cooling solution on the 3rd party board.

One great thing about the nVidia FE video cards is the fact that they exhaust most of the heat out of your case.
The smaller, mini solutions from Gigabyte and Zotac allow you to fit a powerful GPU into smaller PC cases, without compromising or shackling the power of the card.

The downside is that usually the heat generated by the GPU under load is dispersed into your case, so good cooling is demanded - not only on the card itself - but inside the case to boot.