Well, as an AP guy, plant filtration is kinda my thing. That said, I still use a swirl filter to remove (most of) the particulate on my outdoor system, and a "pond" filter w/ a UV sterilizer (as of today). Yeah, it has bio filtration, but I'm not using it for that as much as for the UV clarifying my water. What I really like about the swirl filter though, is that the fish waste collected composts really easily into manure.
On my indoor AP system, I was using a Fluval 406 as a water pump to feed the previously mentioned pond filter as the water source for my display tank, and a really fine mesh bag for the water pump feeding the grow beds.
Before I added my display tank to the system (when I was only using the mesh bag and grow beds), my water was severely tea-stained, though clear. Simply enough, between the uneaten food and the fish waste, the solids were not breaking down fast enough. My 30-odd tomato plants shot up with some incredibly fast growth though.
AZR