Both are really good for the skin and fur. I believe that coconut oil is lacking some of the omegas whereas the fish oil has all that they need.
I use some of both though. I've found that my dogs no longer have smelly breath and their body odor is down A LOT since using coconut oil. I just have them eat a little. Also, after baths, I rub a lil coconut oil between my hands and rub it all over them before brushing. THey both have AMAZING coats and smell lovely. The older dog had horribly skin problems and body odor, both of which are now completely gone.
I've read that coconut oil in the nape of the neck with dissuade fleas, but Im not sure how well that holds true.
When I use coconut oil I try to also use salmon oil, but if you use either/both I would add them in slowly starting with a small amount.
I also noticed an elimination of breath odor when using coconut oil.
fish oil -- source of omega 3 an essential fatty acid and DHA and EPA -- anti inflammatory benefits - good for circulation , eye , brain, neural -- skin , aiding in digestion
coconut oil - plant based , NOT an essential fatty acid - no omega's --- a functional oil which has anti fungal and anti microbial benefits , is anti diarrheal , by passes digestive system, is metabolized by the liver and energy delivered quickly to muscles , good for organ support, adrenal, thyroid , liver . Will detox .
I forgot to add, I also supplement with vitamin E when I give an oil supplement, unless the supplement already contains added vitamin E.
You can read more about this here: DogAware.com: Supplements for Dogs