Plants can be fed organically ( avoiding the use of pesticides, using organic matter to provide nutrients), inorganically ( using chemical fertilizers ), or soilessly when the roots are fed by a hydroponic solution or bathed in an aeroponic mist. Which of these methods leads to the best plant health, and does this also translate to highest nutrient density?
There is not evidence either way about which taste better, and which have more nutrients. However, organic farming is generally associated with sustainable techniques which reduce or eliminate the amount of artificial inputs into the system. So if you are conscious of things like that, then organic is the way to go. I personally am an organic advocate, but I don't proselytize because it just hurts the movement to do so.
There is some evidence which suggests that food produced organically in soil has more nutrients than food grown non organically. With regard to hydroponics, I don't have any information, but given that a lot of fertiliser used in hydroponics is of non organic origin, then likely it is lower in nutrients. See link below for info on soil grown crops, organically grown and non organically grown
It's certainly true that fruit and vegetables these days do not contain the same levels of nutrients as they did 60 years ago - I can't quote this with any certainty, but it was something like, the nutrients in one orange 60 years ago are equivalent to 3 or 4 oranges today. An explanation for this is likely to do with growing methods and a switch to chemical fertilizers by producers, whereas organic growing concentrates on keeping the soil healthy rather than feeding plants directly, but it's something I've been meaning to do research on, particularly with new indoor, year round growing methods in soilless (though not necessarily hydroponic) mediums using LED lights being successfully trialed and eventually available commercially.
From a health point of view, foodstuffs grown non organically will have some nutrition - it just might not be optimum nutrition.