The biggest advantage is it gives the folks who sell tying materials more products to sell & us tiers more variety to tie with!
Seriously, I don't tie many trout flies now, ( I tied commercially for 15 years) but for most nymphs I tie I also use rabbit. I tie a lot with rabbit anyway, bass flies & such so I always have some on hand. I make a point of keeping my trimmings & using the hair for dubbing. I hate wasting anything!
I've tied with just about every natural, legal material possible. They all have different properties, and some are probably better than others for specific patterns. But, for the most part it boils down to what you like to use.
Fur such as Muskrat or Beaver, being water animals, has natural oils in them that make them float well, so they work well on dry flies, but can also be used on nymphs as the fur traps air bubbles well, which can give the fly a different appearance than the fur such as rabbit that just soaks up water. Fur such as squirrel has a lot of stiff, spiky guard hairs, which can give fly patterns very "buggy" appearances. Again, it's really what you like & what you're trying to get the pattern to do. All such materials can be useful.
I've tied patterns like Hare's Ear's with things like Bobcat fur, and frankly, the appearance was almost identical to rabbit, and the fish didn't care either. They still ate them.
I agree with what stimmy7 posted about the bead colors, but, nothing is set in stone. I also use the different bead colors, and many times just depends on my mood. I do however feel in some conditions, a shiny bead can be advantageous, just as a black or dull bead can be. The best thing to do is try a few different ones & see how the fish like them. IMO, there's nothing wrong with having some variety for when you need it.