Well, I haven't really done much research specifically on the differences between fish waste and worm castings, but I can take a few educated guesses. One, I would say it would depend on what you are feeding your fish and your worms to have a material difference.
In my mind, and this is just an informed stab-in-the-dark, I would say the difference would be the beneficial bacteria that is present in worm castings. Worms help process things that are being broken down and are decomposers. As organic matter passes through a worm's gut, beneficial bacteria are added to the castings, while removing a good number of potentially harmful bacteria. Fish, on the other hand, are not in the same class of creature as worms and I don't think their digestive system has the same effect on waste.
Interesting. However, I read that Dr.Lennard seems to imply that aerated fish waste and aerated worm castings (worm tea) would undergo the same process with similar/same bacteria doing the same kind of work. In other words, worms are unnecessary to make "worm tea" or rather "fish poop tea."
I don't know if my interpretation is correct but that is what I take away from reading this article.
I would think if you add xyz to a system (where xyz is the food) or feed xyz to your worms, you will never get more or less than xyz as your output (plant food). Although more of xyz will be stored in biomass with worms. Worms may be more or less efficient than no worms, but essentially everything breaks down via bacteria and becomes plant food.
I guess the main difference is that worms have a wider diet than fish an therefore would produce a richer nutrient profile.
So would you agree with the following: Assume all conditions the same, including same fish feed and in the same growing conditions, worm casting tea produced from worms that consume fish poo would be materially similar to aerated fish poo tea with respect to benefits and drawbacks to a given aquaponics system?
I would agree with that hypothesis. It would be interesting to test. Worms in aquaponics media beds are generally used to break down material that could go anaerobic because people have too many fish in their system for the poo to break down in the given volume of media they have. They help with efficiency. Maybe the bacteria they hold are also more efficient in breaking down one form of matter into another than nitrosomonas and nitrobacter, thus making certain things available to the plants that might stay locked in another chemical form. Again an interesting Hypothesis to test.
"The law of conservation of mass, or principle of mass conservation, states that for any system closed to all transfers of matter and energy (both of which have mass), the mass of the system must remain constant over time, as system mass cannot change quantity if it is not added or removed. Hence, the quantity of mass is "conserved" over time. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form, as for example when light or physical work is transformed into particles that contribute the same mass to the system as the light or work had contributed. The law implies (requires) that during any chemical reaction, nuclear reaction, or radioactive decay in an isolated system, the total mass of the reactants or starting materials must equal the mass of the products." Wikipedia