In an objective-based view, one can say that hydroponics and aquaponics are simply different routes to the same destination; growing plants without the use of soil. From my experience the more nuanced reality revealed two niches that better suited one or the other method. Of course there are always exceptions to the rule, but generally hydroponics is better suited to massive commercial food production facility especially when the sizes exceed 4-5 acres. Hydroponics allows farmers to fine-tune their nutrient formula to achieve incredible consistency in their quality and quantity while maintaining a highly sanitary environment. Aquaponics, on the other hand, forces farms to divide the focus between the plants and the fish. Large aquaponic farms must devote a large amount of time, money and resources to keeping the fish healthy and producing consistent nutrients. Aquatic diseases are a major concern and a large investment must be made to control temperatures, otherwise the drop in temperature will slow down the metabolism of your fish.
Aquaponics shines in agricultural categories such as non-profits, personal business sub-three acre farms, hobbyists, commercial decor/aesthetics, and applications where emphasis on natural biological systems in harmony is desired. The small 24 m x 44 m system could easily boost a communities' access to healthy vegetables, fruits, and fish for very little individual financial contributions while serving as practice grounds for budding agriculturalists and environmental biologists. The real significance of aquaponics lies in its unparalleled sustainability; even more so when in conjunction with other natural cycles such as composting, outdoor gardening, and chicken keeping. Food waste from harvests can be used to raise black soldier fly larvae for chickens and the fish. Solid fish waste and chicken waste can be returned to composting or used in the outdoor garden. Solar can be introduced to take small systems off-grid, effectively un-tethering a family's (or community's) dependence on commercially available food.
Finally at the sub 10 gallon range, hydroponics takes the lead once again due to the convenience of measuring out the perfect concentrations of nutrients for your plants. It is possible to grow a healthy bibb, kale or arugula in 2 L bottles using the kratky hydroponic method. This makes it optimal for absolute beginners to begin growing their own food at home and serves as an excellent introduction to soil-less agriculture.
Regardless of the method, I am certain the future will see a rise in both methods to sustain the growing demand for local, healthy produce in a more environmentally-conscious market.