There are likely some small differences in amounts of vitamins and minerals as well as levels of fats such as CLA, but other than that, there will be little variation.
Quite frankly, I would be more worried about the fat percentage and lactose. Go whole or go home.
There are some ‘reports’ and ‘studies’ that try to show organic dairy as being superior to normal stuff, but they are usually over-extrapolated or assume the absolute worst cases for normal dairy and the best cases for organic.
What I do:
I personally don’t drink too much milk (less than 2L a week), but when I do, it is a mix of organic and non-organic - I rotate through different brands also for the slight taste variety.
For cheese, I don’t worry - though I usually go with European hard cheeses so I am consuming European milk products which are a little closer to organic than say US milk.
And with yogurt, I usually get organic because I can get a 1.75Kg tin with 8 types of bacteria in it for the same price as non-organic yogurt with 2-5 types.