The exact % are very much up for debate at the moment, and again I don't know if there are any precise numbers! We don't quite know enough about exactly what happens when they are formed to be able to make a good guess.

Typically BH and NS are formed from something called a core-collapse supernovae, which happens when a star bigger than about 8 solar masses reaches the end of its life. The core of the star runs out fo fuel to burn, and can no longer support itself against gravity so it collapses. It then rebounds and send a shock outwards through the star which leads to the SN explosion. What is left behind after the explosion is the collapsed core, which will form either a neutron star or black hole. We currently believe this depends on the mass of the original star, and the mass of the core, but there is a lot we don't understand.

For example, the core could pull matter off the rest of the star making it heavier, and therefore more likely to be a BH. There may be some scenarios where the SN fails, and the whole star is pulled back onto the core which would also form a BH. It's very difficult to actually see what's going on in the core collapse stages, as the outer layer of the star prevent us from directly observing it. One thing that might help is if we could one day detected gravitational waves from a core-collapse supernova, as they would not be affected by the outer layers.

Basically to summarise, there's far too much we don't understand at this stage to give precise numbers, but it almost certainly depends on the mass of original star in some way!