Welcome to YT! Great question! I personally would never feed Science Diet or Eukanuba to my dogs (but I used to until I researched it). Vets recommend these brands-but realize that many vets get grants from these large companies, so that may be part of the reason they recommend them. It's difficult not to agree with and/or trust the vet when they recommend foods, but after doing my own research on this, I chose the best options that work for me and my dogs.
Check it out at
www.dogfoodanalysis.com
You'll find that most SD foods are not very high quality dog foods. A 4 or 5 star food is recommended by most YT members for yorkies. Skip the 6 star foods, as they are too rich for toy dogs, and meant for large breed working dogs.
Many members feed Canidae, Innova, and others. I fed Blue Buffalo, but have now switched to homecooking/home prepared food for my two.