Organic milk has a bunch of regulations around it. Some are a bit silly. For example if your cow is sick and you treat her with antibiotics you can not sell the milk until it is out of her system with regular milk, with organic milk you can never sell her milk as organic again. So you might as well send her to be made into hamburger.
Aside from that the organic cow must have access to pasture 120 days a year. Most cows have that anyway because having the cow out on pasture means less clean up and lower feed costs.
Now organic cows have to be fed "organic feed" which is not necessarily better just raised according to the rules to make it organic.
The additives and minerals added to the feed are exactly the same.
In short, organic milk, buy it if you like, if you need it to last longer or you like the flavor. But there is no major differences between it and the regular stuff.
I buy regular 1% milk and use a gallon before it goes sour. I do find that the taste varies from good to almost bad depending on the producer.