It's a x16 slot at x4 speed. As long as it's a pcie slot, it will work.
So in that case, due to the fact that my GPU is also going to be Gigabyte's, is there a slightest chance of it being more compatible with Gigabyte mobo than Asus??
It may seem rubbish
.. and apologies if it does... but I'm not looking at it from the performance perspective of course, but better... rather optimum compatibility.