Is Nutro Natural Choice Cat food good for Indoor Cats?

I have been thinking of switching my cats to a healthier cat food, they currently eat Fancy Feast and love it, but thier fur is dull, sheds ALOT even after I brush then regularly, and even though they looove eating it they end up throwing it up shortly afterwards. After a visit to the vet I was told to feed them either, Iams, Eukanuba, Nutro, Royal Canin, or Pro Plan from Purina. I read the ingrediants of all the cat foods recommended and only Nutro, and Royal Canin did NOT have by products. I know Nutro makes both MAX cat and Natural Choice, but I have a finicky cat that loves fancy feast, so which do you think would be a good choice?