You can store music on the watch, but the sync is so slow and the data cap is 2 GB that unless I want to listen to the same playlist on infinite repeat its not viable. You'd also need bluetooth headphones, which is a purchase I don't feel I actually need... generally when running I'd rather be alert of surroundings less I get hit by a truck while jamming to a favorite track.
My use of music controls on the watch has been this: phone is sitting around office or home and connects to sound bar, I can leave phone charging somewhere while reading / studying / drawing and if I want to change tracks or volume its a flick on the wrist. Otherwise while in the subway + listening via headphones on a crowded train, can change music while keeping a grip on subway poles.