What is better, removing fish waste with a mechanical filter or draining it and put it in your garden or pumping the fish waste into the growing bed with an growing media?
After all we are after the nitrate to make the plants grow. If the fish waste is pumped into the growing bed is there a possibility that the fish waste turns into anaerobic material and hindering proper flow?
Would the fish be healthier without the fish waste being constantly in the water?
If your system is designed with the appropriate amount of media beds for the fish load, then you want the waste to go to the media beds to provide the nutrients for the system. If you are running a system that needs the solids removed, you have to spend far more money on fish food to get the same amount of nutrients for your plants. However, if your media beds are not sized appropriately, and the fish load too much for them, then you could get nasty anaerobic spots and it would be healthier to remove the solids.
Aquaponics is all about balance and there is no single best way to do things. Only perhaps a best way for a particular situation or goal. If you are going to be removing solids then the system needs some additional elements and it will take the regular extra labor of doing that solids removal since if you are catching solids some how, you will have to clean that filter or settling tank before it clogs or becomes anaerobic itself and probably have a degassing method after it to keep any of the bad gasses that might happen as the solids collection does become anaerobic to escape before the water is sent back to the plants/fish.
I've done well having twice as much media bed as I have fish tank.