Yes, it is healthier. Organic animal products do not contain pesticides, antibiotics, or hormones, and when one uses grass-fed meat or dairy, it has the effect of actually reducing cholesterol ansd serving as an anti-inflammatory, which helps in yeneh machla prevention. By produce, however, there can be serious problems as far as sheratzim go. For shomrei kashrus, it would be best to only use organic potatoes, apples, etc., basically any fruits and vegetables you eat the skin, but to use non-organic berries, lettuce, cabbage, etc., and wash it very well, due to the sheratzim factor, but using organic meats and dairy falls under shmiras haguf, and to me, is a chiyuv. The problem is that I do not know yet of one cholov yisroel grass-fed organic dairy in the country.
Menu