Restylane Vs. Fat Grafting for Under Eye Hollows?

Restylane or Juvederm, both hyaluronic acids, are commonly used, off-label (not FDA approved for this use, but doctors may legally perform the procedure) for this purpose.
Fat injections may give you a good result but, there are different ways that both of these fillers are done by different doctors. Some inject over the muscle, and there may be larger chance of visible bumps.
The nice thing about Restylane or Juvederm is that if there is too much filler injected, it can be dissolved by injecting hyaluronidase. This also can be used in case of serious complications, such as a plugged blood vessel, whereas there is no equivalent of hyaluronidase for fat injections.

The key is not the procedure but who does the procedure.  Either might be appropriate for you -- and they are not the only options.  There are other fillers, biostimulators and devices that might be approrpriate.  The addition of the right cosmeceuticals can also make the difference in your results.  My recommendation is that you seek a consult with an experienced physician board certified in a core cosmetic specialty like dermatology.  Review your concerns and your goals with her and have a clear discussion about your options, risks  and benefits.  I hope this helps answer your question. Best wishes.