I’ve never tried a moscow mule, but I’ve sampled several ginger beers, and there’s some pretty extreme variation within the style, ranging from those that are almost gingerale, to those that are extremely spicy and dry. My personal preference is Old Tyme ginger beer, but it’s dry enough that I don’t know if it would pair well with actual lime juice - I might consider Rose’s Lime Cordial to make something a bit more drinkable