Yes, you can absolutely use an ATI (amd) card with an Intel CPU.
the advantages and disadvantages are very much a matter of personal opinion, and you will get many different opinions.
ATI (amd) cards are generally less expensive and faster more powerful cards
nVidia cards are a bit more expensive and have better drivers that actually let them perform better than their ATI counterparts (usually)
performance is measured in benchmark tests, which measure far beyond what a person can differentiate.
Bottom line, either card will work equally well (plus or minus a few frames per second) pick one that works in your budget.
If you meant advantages of Sandy Bridge CPU with either AMD/ATI GPU versus nVidia GPU then the primary advantages to nVidia GPU(s) are: Scalability (multiple GPUs), cost per FPS, 3D, PhysX, longevity, lower temps, better efficiency, etc to name a few advantages. Today...Tomorrow only testing and reviews will tell. ATI has advantages too like easier to CF, AA and higher sampling details.