A black hole has the same escape velocity as a star of the same mass, as long as you are well outside the swarzchild radius. Inside or near it, the effect of general relativity makes things very weird.

In case of mostly anything else, Newtonian physics apply correctly, and the relevant thing is mass (and distance from the center). The escape velocity from a body is sqrt(2GM/d) where d is the distance from the center of mass, M is the mass of the object, and G is the universal gravitational constant.

Note that if the sun was replaced with a black hole of the same mass, the orbit of the earth wouldn't change.