Many of my veggies do great in aquaponics including tomatoes with the addition of minerals, but all of the peppers from bell too jolokias and the entire squash family do much better for me in potting soil or commercial planter's mix
However, I was surprised to have the five Yacon plants, which are a root crop do twice as good as the five Yacon planted in containers! The ones in my system, which include a lot of red wiggler worms, was in a fast draining media by Pro-mix, connected to a drip system. All of the leafy plants excel in aquaponics.
Nice set-up