In an aquarium the fast growers do best to take up an exces of firts.. Aquaponics has its focus on the helophytes.. Im planing to build me a little one for my aquarium, but im still brainsorming about the decorative part.. But i rather won't take the chance of never refresh some water in a small tank with an aquaponic. For setups like that you rather need very large water mass so it can create its own bio system with enough buffer capacity. Small tanks don't have so much buffer and will become much faster unstable.
By the way.. Most aquatic plants available to us are swamp plants and not fully aquatic. So some of them maybe could do a nice job in an aquaponic as well. This is a case of doing homework and trail and error, for me that is i mean.