Gravitationally, nothing would change if the sun was replaced by a black hole of the same mass, at least for objects above the surface of the current sun. But b

Gravitationally, nothing would change if the sun was replaced by a black hole of the same mass, at least for objects above the surface of the current sun. But being 1 kilometer above the event horizon of that black hole would be very different to being 1 km above the surface of the sun. As the radius of a object shrinks (but with mass held constant), the _surface_ gravity increases. Remember that the pull of gravity decreases with the square of the distance away from the object. With a smaller object, you can get a lot 'closer' to all that mass, so gravity is stronger at its surface.