Which would be more likely to collide, stars with stars or galaxies with galaxies?
Neither or both depending on how you look at it.
Stars tend to exist in a binary setup. That is, two stars orbiting about each other. Our star, the sun, is an exception although there is discussion that maybe a long ago twin died and is still out there somewhere, just unseen.
If one star has considerably more mass than its twin, it will slowly draw mass away from its twin before finally killing it off. That is about as close to a collision as you are going to get.
Some astronomers believe the Milky Way we see today is actually the result of a long ago collision with another galaxy. Regardless, in the distance future we will "collide" with the Andromeda galaxy. Collision is a very loose description because of the great distance between stars, when the two galaxies do come together, it will be more of a melding than a collision. That would be true of any galaxy "collision" therefor.