You can most likely ward off a lot of the muscle breakdown that occurs during fasting with a BBF. BB is a good source of easily assimilated amino acids. It requires virtually no digestion and thus it doesn't interrupt the fasting process, whereas even a piece of fruit is considered breaking a fast. In addition, a BBF will actually give you decent amounts of nutrition. Bone broth/gelatin is also soothing to the intestinal tract, but any type of fasting does that also due to a break from digestion. BBF just does it more. A BBF also provides electrolytes so it's significantly less dehydrating than a water fast.
Plain water isn't particularly hydrating and for those with kidney issues, a water fast is not a good idea. A water fast will probably encourage a higher degree of autophagy and may be better for detoxification purposes. But supposedly BB increases bile secretion, which is a big portion of how the body digests and detoxifies.
And plain water is just so boring. When I drink bone broth or eat gelatin it at least feels like food.
I generally fast for 4 days and then if I'm feeling up for it, I'll go for 7. You're not really hungry after the 3rd day on any type of fast. Just listen to what your body is telling you.
Note: I'm biased towards bone broth fasting obviously.
To answer your question, the benefit of a total water only fast is that your body goes through a healing crisis. This doesn't happen if you're ingesting anything other than water. Sure it's a crisis that you're eating only broth and therefore your body has to go to its own stores of fat for energy, but not as much as if it had to provide sugar for your brain and blood sugar level, and all the fat for your energy level. Different amounts of enzymes are required to pull this stunt off.
That's why it can be dangerous to do this kind of fast. Some people simply don't make enough of the enzymes to support their blood sugar levels correctly, or to make enough ketones to maintain energy levels. If you're one of the genetically unlucky who can't make enough of the right kind of enzymes... you'll instantly know it when you water-only fast. In a couple of days, you'll be vomiting and unable to think and hardly able to move. Therefore if this is your first fast, make sure there are people home who can help you, and have broth on hand to help you out of the emergency.
If you are able to water fast, you can look forward to losing 1 lb a day if you're obese and if you're good at controlling food intake after the fast, then you will keep it off too. Ingesting anything while fasting will slow this process, but it will make it easier to fast because the unpleasant achy and tired feelings will be reduced. Bone broth is a good thing to keep on hand whenever water fasting just in case you can't go to sleep or the aching gets too intense.
Honestly I take high DHA fish oil, a vitamin, and aspirin with Bone broth once a day while fasting. The fish oil + aspirin is a known combo for fighting inflammation, the DHA is used by the brain, and the bone broth spares my muscle. But once I am deep into the fast, I can go a few days without it.
People can safely fast (if they have good genes to make enzymes) for 1 month, maybe 2, on water only. People have fasted for 6 months on water only, and then died. I read that in the Fasting book by Dr. Fuhrman. Obviously I don't take his book as gospel, but it has some good info anyway. So does his research website.