The black hole would tear the star apart. The star's more powerful gravity would cause it to pull the black hole in yes, but once they get close to each other, the game changes from overall gravity, to tidal gravity. The black hole will start tugging on one side of the star much harder than the other side, so one side will be accelerating towards the black hole much harder than the other. Anything that ends up inside the event horizon of the black hole, increases the mass of the black hole, so the black would would simply start sucking in the star when it crashed into it.
A black hole just slamming into a star is unlikely, most of the time objects in space sort of glance each other, this would probably cause the star to be torn apart. A star's gravity holds it together, at it's surface though, the star's matter is far away from the center of mass, so it's held there strongly, but not as strongly as a black hole. The escape velocity of a star is probably a few million miles an hour, the escape velocity of the black hole is beyond the speed of light.
The black hole's mass isn't what's scary about them, it's about how densely packed all that matter is. You're standing on the surface several octillion tons of matter right now, but if you were at the surface of a black hole of the same size, it'd tear you apart atom by atom.