Yes.
They taste different but not so much because of the type or color of beans, but the method of preparation.
While generalizations are always fraught with errors, it can be said that Korean JJM (or zha jian mian, ZJM) typically uses fermented black paste, or chunjang, as the main and the primarily ingredient in the sauce (excluding things like pork, radishes, potato, etc).
Chinese (or Taiwanese) versions, by contrast, use tian mian jiang (甜面酱), which is a thick, dark brown sauce made from wheat flour, sugar, salt, and fermented yellow beans. But in addition to that there are generally other condiments added to the sauce, ranging from hoisin (or oyster) sauce, to soy sauce, to even miso. And of course things like dried shrimp or conpoy are quite common to give the sauce that extra dimension of briny umami.
Which is better? No better, just different.
Try them all. Then go and find your inner JJM (or ZJM) and then announce to the world that you have become one with the fermented bean paste