Organic vs inorganic is a pretty broad subject. People have different measuring sticks... even when it comes to the government. Some states allow some hydroponic systems to be classified as organic, and some states require that it be grown in soil to be classified as organic. (How you can have a 100% organic hydro set-up is beyond me, but that's another topic...)
As far as science can tell, plants need nutrients, and so long as you give them to the plants in a form they can take-up... there is no difference.
http://www.ncbi.nlm.nih.gov/pubmed/12696944
The only negative research paper I've seen was done on leafy greens, and they had much lower beta-carotene and lutein than the soil grown plants. But then again, they weren't given direct sunlight either... the researchers even acknowledged that.
On the other hand, I can find lots of papers giving the benefits of hydro.
Ask a grower though, and it's one spectrum or the other. Most either hail hydro as the next coming of christ... or curse it with every breathe.
We've been experimenting with hydro since the 1600s (Francis Bacon actually experimented with it...)
We've been growing with hydro set-ups since the 1930s...
http://babel.hathitrust.org/cgi/pt?id=uc2.ark:/13960/t51g1sb8j;view=1up;seq=1
And we haven't found anything bad/wrong/dangerous about it yet.
Oh, and as for quality... lay out 8 or 10 strains for someone to try. Most higher-end dispensaries will be able to tell you if its grown in hydro or soil, as they know their donators fairly well. Have someone taste test all 10 and tell you which is hydro and which is soil. I've done it. I've made my friends try it. You can't.
As it is with most things... it isn't what's grown that messes up, it's the grower. You can screw the pooch in both soil and hydro and come out with terrible plants.
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The question of *can* something be used is also different than *should* it be used. *Can* you use your homemade worm casting and shellfish meal tea in your hydro set-up? Yeah, throw that shit in. *Should* you? No probably not, as your pumps and hoses will quickly get clogged from deposits in most cases.
As for soil and synthetics... soil is just a medium. Sterilized soil and RO water might be able to grow a plant, but it isn't going to be what you are looking for. Whether you are using a homemade tea, or your favorite go-go juice from the hydro shop... it still needs something. (Yes, even you TLO guys still add in what you need, you just do it while making the soil.)
Plants literally have a chemical recipe for success. Follow the recipe, and your plants will come out fine, whether it's in organic soil or the salt hydro of doom.
And for the record I grow in Happy Frog with Botanicare PBP, CalMag, and Molasses only. Just before the synthetic witch-hunt begins...