Hi and welcome to the Gigabyte Forum.
Well each side , AMD and nVidia, has thier own followers and often they won't be swayed either way. Personally I go for whichever gives the best bang for buck result. At the moment I would suggest AMD as the better buy, not just because of value but I feel there are a lot of issues at the moment with nVidia cards.
If you are looking for sheer power then probably the nVidia 580 is the way to go (unless you want to wait for the 590 dual chip board), but cost and power requirements are prohibitive. Also noise is a major drawback too unless water cooling.
A lot depends on your budget and the type of use it will be put to. The AMD boards are certainly more affordable and there isn't much difference in terms of output. They also offer "Eyefinity" which enables the use of several monitors in a sort of surround view configuration. This is quite impressive and can give a definite advantage when game playing, apart from the "bragging rights"!
I hope this helps a little and if you have any specific questions please post back.
