I have been trying to find info on nutrition for some time but the available resources (I am not affiliated with a university so only open papers and abstracts are available) are limited. I have not been able to find a lay person readable study on the differences between freshwater vs saltwater inverts and begin to suspect, as you are finding, that the subtle differences are unimportant unless, perhaps you are attempting to breed and raise the young. The studies I DID find compared feeding saltwater fish vs crustateans (done in South America, unfortunately, I did not keep a journal of references or if I did I can't find the post
). The studies were initiated to see if it was viable to raise octopuses as a food source on something cheaper than crabs (but still saltwater). The results showed that octopuses did not grow as well fed entirely on fish and the discussion/summary indicated that supplementing and further research would be necessary. One of the noted thoughts was that crabs contain usable copper (vs lethal) that may be needed for proper blood development. Effects of freshwater fish or inverts was not attempted and not relavent to the intent of the studies.
As an asside, most of us feed (those not living near the coast) grocery store shrimp to our octopuses (as well as frozen fresh water mysis). If you read the fine print, most of these are freshwater raised. However, from what I could find in the net, freshwater shrimp are actually saltwater shrimp raised in lower salinity but in the normal to high SW PH. Neal and I go looking for wild caught SW varieties but those that we find contain sulfieds for preservation. I have not seen this noted on the FW ones but they may also be treated. We feed as much variety as we can find in hopes that we avoid a build up of the negatives of any one of the options. When I next get the opportunity to try to raise a few young, I think I will experiment with food to a bit to see if I can get a result that may be worth studying.
Trying to give this kind of a discussion when someone asks what to feed their octopus, however, presents misinterpretation problems for the new ceph keeper so my initial response is to stay with saltwater animals. Freshwater fish, for example will not provide a proper diet at all but if an octopus eats a freshwater fish it will not kill it (assuming it was not treated with copper).