Apple juice will give you very little additional taste, but it will sweeten your smoothie. Especially filtered apple juice has a rather subtle flavor which is easily covered by other fruit flavors. Juice producers use this to make their juices cheaper - if a juice advertises 100% fruit, and a flavor from an expensive, non-juicy fruit like strawberries, it is usually a blend of a small amount of strawberry juice and a large amount of apple juice (this is not fraud, the ingredients are listed on the package if you care to read it). Apple juice is normally made from low-acid apples, and it tastes quite sweet, so it is useful not only for bulking, but also for sweetening blends made with sour juices like elderberry, cranberry, etc. In a smoothie, it will have the same effect as in a juice blend, plus a diluting effect, as it is less viscous than your other ingredients. It won't amplify the flavor of the smoothie, it will even reduce it, as sugar tends to suppress other flavors in general. But the reduction won't be too big, and you might find the overall result better if you are accustomed to heavily sweetened food. You can also remove the sugar if you use apple juice - I wouldn't put it there anyway, even without juice.
Orange juice is much more acidic than apple juice, and it has a stronger aroma. It will add an orange flavor to your smoothie. I would count this as an advantage, because orange flavor goes especially well with bananas and is OK with strawberries too. It will also make the smoothie taste more sour, and again dilute it. Overall, the effect will be pleasant. As for what constitutes "overpowering" the taste, I think this is subjective. You should just experiment, adding a the juice in small proportions, until you have achieved the ratio which tastes good for you.