I think I would buy frozen over our supermart fresh.
Two things to consider, Teresa.
First off, very few inland supermarkets actually sell fresh fish. Most of the time what you see in their counters is previously frozen. And, technically, it should be marked as such.
Second, nowadays, frozen fish is actually fresher than fresh fish. Unless you personally buy it off a day-boat, even along the coasts the fish you buy in a seafood market is at least four days old by the time you get it.
On the other hand, FAS fish has been caught, processed, and flash-frozen within two hours. So long as you defrost it properly, it is as good, or better, than anything you'll find masquarading as "fresh."
The only downside to buying frozen fish in the supermarket is packaging. Depending on the brand, you often don't know what's in the package. F'rinstance, we once bought a package of "cod filets." What we found was five pieces, of different sizes and shapes. So keep that in mind, too, when choosing frozen seafood.
They have taken the oath of the brother in blood, in leavened bread and salt. Rudyard Kipling