Dan Barber goes into this topic in some depth in his book "The Third Plate".
He looks at nutrient density, which is difficult to measure without some serious scientific diagnostic equipment. Not all carrots are equal. An
apple a day may or may not keep the doctor away—it just depends upon the
apple and the amount of nutrition offered by that apple comparative to all the other apples that are being grown in all manner of ways.
Barber's simple (but not simplistic) thesis is that better tasting fruits and veggies are packed with far more nutrition than those that don't taste as good. The easiest measure would be brix levels. Just squeeze a drop of juice out of fruit or veggie and you'll be able to measure the sugar content. Obviously, a sweeter orange or plum or whatever will taste better, or more accurately, capture the complexity of taste produced by those sugars and starches. But not only do they taste better, but they're much better for you, and you're more likely to eat more of those better tasting veggies (and thus, less other stuff that isn't as good for you).
Now that organic produce is being grown on a mass scale, we are getting the phenomenon of "shallow organics". Yes, those beets or kale or pears were grown "organically", but that's not to say that they were grown naturally with lots of
compost, mulch, in a poly-culture with animal integration and fresh rain water. Something grown on a commercial organic factory farm will not have the nutrient density of that same fruit or veggie that is thoughtfully grown by someone else. Don't believe me? Then trust your taste buds. Simply take that pack of organic carrots from Whole Foods and compare then to carrots that you grow yourself in a bed that you've been amending for 3 years with homemade compost, cover-cropped in the off-season, planted in a multi-species cocktail of other plants, and lovingly fertilized with manure from your homegrown
chickens.
Night and day. You can't even begin to compare the taste.
And nutritionally, it'll be night and day. That carrot (or beet, or artichoke, or cabbage or lemon or peach or whatever) will be much more healthy than what you'll buy that was commercially grown. At least 90% of the time that will be the case.
The same goes for the lovely eggs that my happy
chickens lay. Nutritionally, they are so much better for you, and taste-wise, they are clearly superior to anything you'll ever buy at a store. Why? Because the girls are getting fresh bok choi and weeds and bugs and veggie scraps daily. They are scratching in real dirt, looking for real worms, drinking real rainwater, parading about in the real sunlight, and living a wonderful life.
Healthy and abundant microbes (bacteria and fungi) produce healthy soil.
Healthy soil produces healthy plants with nutrient dense fruits and veggies.
Nutrient dense produce tastes better.
Healthy, tasty produce is eaten by humans and animals and they, in turn, become healthier.