Fuming is not the perfect colorant for every situation and wood species, but where it does work, it works very well and can give a superior finish to stains or dyes. Stains obscure the surface of the wood somewhat. Worse yet, on ring-porous woods like oak, pigments collect in large open pores, making the rings very dark and overly pronounced. The effect is quite unnatural and looks to me like thousands of dark specks sprinkled across the surface. Aniline dyes do a better job than stains, but they're also rather labor-intensive and can be very tricky to apply well.
Dyes also fade over time, especially in direct sunlight.
Fumed wood is colorfast. The thing I like best about fuming is that what you see after the process is still only the wood, just as clearly as before. It's just darker. That's because the ammonia reacts with tannins that are naturally present in the wood, actually changing the color of the wood, not merely adding a superficial layer of color. Another thing I like about fuming is that it's virtually foolproof.