It definitely tastes milkier in general. In addition, raw milk available for purchase usually comes from a single source, as in one farm, one small herd, even one single cow, so consequently there can be a lot more variation in flavor than you'd find in grocery-store milk. What the cows are eating, the time of year, the weather, the stage of lactation, how quickly the milk is chilled, how it's stored, even the breed of cow, can all change the flavor of raw milk significantly. So even if you do try it from one particular source and don't like it, that doesn't mean all raw milk will taste the same. If that happens, it's worth trying other sources to see if the flavor is more to your family's liking, if raw milk is something you want to incorporate. Milk from the grocery store is typically pooled from thousands of cows from multiple dairies before it's processed (pasteurized, homogenized, etc.) in centralized facilities, and that pretty much eliminates any variation in flavor, and of course the processing removes and changes flavors as well.
I have a cow, and the difference in her milk's flavor between when she's eating primarily alfalfa hay and when she's getting more green grass or grass hay is pretty dramatic.