If you are one of those people who does not eat oily fish, the advice to start doing so does seem to have some solid evidence.
See this article, for example. Whether the same benefits can be gained by consuming fish oil supplements has not (I think) been established.
Pretty much the only argument for the supplement over the actual fish is that for wild, ocean / sea caught fish, there may be quantities of pollutants (mercury, dioxins etc.) that are not found in the highly refined supplements we see in the shops. And we can assume (can we?) that farmed fish swim in waters that are less polluted (but with added antibiotics?).
But for an adult, the quantities we are talking about might not matter too much. But for children, especially toddlers, and definitely for mothers who are planning to conceive or who are pregnant, supplements would be safer.