in my opinion fish oil is more beneficial than flax oil, since the fish oil contains active omega 3 fatty acids that are immediately usable to the dog's body, whereas the ones contained in flax seed have to be transformed and some dogs don't even have the capacity to do so. they may still benefit from the increased amount of fat in their diet (e.g. soft, shiny coat), but do not get the full therapeutic effect of the fish oil.
the amount you'd want to feed of the fish oil depends on what kind of fish you include in the dog's diet, as only ones that live in cold, salty waters supply high amounts of the highly beneficial omega 3's. in addition to that, good quality fish oil (doesn't have to be salmon necessarily) has many of the impurities removed that you would still find in the fish in their natural state, so you can feed higher amounts without possible problems from contamination.
it's best to feed a human grade fish oil supplement, as the ones specifically produced for the pet market are not subject to the same strict quality control.