Hi Joanna, the bullet solver is the older legacy simulation system in Cinema 4D. It was often very slow, unstable and hard to work with (especially for cloth and soft body simulations).
The new system is much better, it utilizes your GPU so it can simulate much much faster. The new unified system also allows interaction between cloth, soft bodies, rigid bodies, particles, pyro etc (which bullet did not do so well).
I think the new system is better in every way so I cant see any need to go back to bullet.
I’d say use the new system (especially if you have a decent GPU) and only use bullet if you’re struggling to get your simulation the way you want it, bullet may work better in certain situations.
I actually switched back to bullet once when creating this effect: https://cgshortcuts.com/expanding-sphere-effect-in-cinema-4d
Because I couldn’t achieve the effect in the new version.