Would fat grafting or fat repositioning deliver better results in the long term? Hoping to address lower eyelids (photo)

Different surgeons have different perspectives on this, but I would recommend lower lid blepharoplasty with fat grafting based off your pictures. It blends the lower lid and cheek to a more youthful contour and appearance for a number of reasons. I'd recommend finding a Facial Plastic Surgeon, Oculoplastic Surgeon, or Plastic Surgeon in your area who specializes in lower lid blepharoplasty and fat grafting to discuss your different options.

Often a combination of procedures is helpful for the area under the eyes. The orbital retaining ligament is strongly attached and forms a severe groove between the cheek and the lower eyelid when the cheek tissue droops. To soften this distinction, fat grafting can help, although likely the midface needs to be supported back to its original position. There are several different ways surgeons do this. Some extend their blepharoplasty, some do midface lifting and others accomplish midface lifting as part of a facelift they perform.
The lower eyelid is a separate issue. You may have bulging of the lower eye fat pads (a photo with the eyes looking upward or an in-person consultation would be able to evaluate this). Depending on your surgeon's technique these could be managed either with removal or repositioning during a blepharoplasty. Either technique can work well. Some surgeons feel the lift of the midface resolves the issue completely without the need for blepharoplasty.