Blepharoplasty or Filler in the Tear Trough?

I think surgery is the better choice for you and here's why:
You have an abundance of fat that can be used to reposition over the hollow areas under your eyes and in your tear troughs. This method avoids the over-hollowing some patients experience. The fillers are fine but do not last very long and have a high risk of bruising (so does surgery but at least it's a one time thing). Just make sure you see a surgeon who is not overly aggressive about fat removal and more conservative in the approach, preferably to reposition the fat.

It's not unusual for patients with tear trough deformities to request plastic surgical consultation. When this situation arises, a variety of treatment options exist to treat this condition. These include surgical procedures that release the arcus marginalis and the use of injectable hyaluronic acid fillers that minimize tear trough deformities.It's extremely important to individualize the treatment of tear troughs. For this reason, the specific procedure chosen will depend upon the patient's anatomic findings and aesthetic goals.It's important to realize that lower eyelid filler injections are very effective for treating tear trough deformities, but aren't for everyone with this condition. In some cases, the lower eyelid skin is extremely thin and for this reason, injectable fillers aren't always indicated. In this situation, injections may be accompanied by nodules and bluish discoloration. Furthermore, this approach only provides a temporary solution to the problem.It's important for patients with tear trough deformities to consult a board certified plastic surgeon with experience in this area. This surgeon should be able to formulate a treatment plan that addresses your anatomic findings and achieves your aesthetic goals.

Judging from the picture I would recommend transconjunctival lower blepharoplasty with orbital fat translocation to pad the tear trough.  This approach minimizes the hollow sunken eye appearance.  The key is removing yet preserving enough fat to still be able to "pad" the tear trough and make it smooth and natural looking.  When done in expert hands, recurrence of that fat is minimized, however, not zero.