The different milks in my US region (Pacific North West) definitely have different flavors but I have no idea if it's due to what they graze on or other stuff they are fed.

If you are in New York city (especially Manhattan), you can often get RonnyBrook milk at the Union Square farmer's market and various stores around Manhattan - it tastes so much better you might think it's a different class of drink.

It's grass fed; if you buy it in the farmer's market, it's a couple of days fresh; and they care about their cows. I bought a bottle once, which didn't taste as good as usual, and when I told the guy at the market (he actually raises and cares for the cows), he took notes to figure out which cow was unhappy/unwell.

Not affiliated, was just a satisfied customer until I moved out of NYC (and now have no good milk available :( )

Milk is pasteurized differently in the US vs Europe. I’d bet that has the most impact on taste.

To those longing for milk that tastes like something in the US, I'd suggest finding a supplier of Jersey cow milk if you can, a much richer and more flavorful alternative to the Holstein cow milk most commonly available. Jersey cows produce less milk than the Holstein, but its butterfat and protein levels are significantly higher [1]. The cows' diet is going to have the highest impact on flavor regardless of breed, so it's important that they be free-roaming and grass- (and maybe seaweed-) fed, but it's likely that any alternative to Holstein cow milk is going to have a better flavor.

In Northern California, Saint Benoit [2] markets Jersey cow milk and yogurt. The flavor of their milk is incomparable to all others I've ever tried stateside.

[1] https://en.wikipedia.org/wiki/Dairy_cattle#Breeds

[2] https://www.stbenoit.com/