Science Diet is pretty Junky, BUT there are instances where it is necessary.... The thing with vets ans SD, is that the few classes in nutrition they get are sponsored by Hills (manufacturer), and they also get some perks, continuing education, and associates benefits..... so..... vets sell their stuff, and will naturally push it.
As far as by-products, chicken by-product is ok.... The one that is BAD, BAAAAAD is "Meat by-product" and "meat by-product meal".
If I recall correctly though, there is a lot of corn, soy and other grain and junk on SD.... other reasons why you should stay away. It is full of fillers, not much nutrition.
Vets in general do not really know about nutrition, unfortunately..... but that do not mean they are bad vets.... You just don't go there for that- you come here
Please don't judge a vet by the fact that he/she will push SD on you - most of them will... How was the rest of the consultation? Can you check online referrals? Do your neighbors have pets you could ask for referals?
About feeding Raw and dry: NOT a good idea - they have different digestion times, and it can be dangerous, the bacteria from the raw can flourish and be toxic for your kitty, as the dry food digestion is much slower.... So in a way your vet was correct on this...
I am by no means an expert on this, but I did research this route before, and was stopped on my tracks...
Do a lot of research on this, I do think this is not a healthy diet option for your cat.... unless you give the raw as an occasional treat...