Would the moons get struck by asteroids instead of the Earth or would the moons attract more asteroids and make it more likely the planet gets hit?
I don't quite buy JamesK's claim that "the moon only covers less than 0.001% of the sky, and so leaves us vulnerable to 99.999% of asteroids."
That argument would work if typical asteroids 1) came from random directions, 2) travelled approximately straight through the Earth–Moon system and, if they didn't hit anything, 3) departed never to return. However, while these might be decent approximations for interstellar objects, none of them are true for typical near-Earth objects (NEOs) that make up the majority of potential impactors.
In fact, a much better approximation would be to assume that an object that passes by the Earth without hitting anything will return to the vicinity of the Earth some number of orbits later, and will keep doing so until it eventually hits either the Earth or the Moon. Replacing assumption (3) above with this one, while keeping the other two, would imply that the ratio of objects that will eventually hit the Earth vs. the Moon should be approximately proportional to the ratio of the squared radii of the two objects.
Doing the math, this suggests that about 7% of all asteroids with orbits taking them close to the Earth (and the Moon) should eventually hit the Moon, while the remaining 93% should eventually hit the Earth.
Of course, this is still neglecting the gravitational dynamics of the system and the fact that orbits of typical NEOs passing through the Earth–Moon system aren't quite straight lines. Still, it's at least roughly in line with various claims I found by Googling, such as this passing mention on a NASA web page that "about twenty asteroids strike Earth for every one that strikes the Moon".
Adding a second moon of similar size as the one we already have (and ignoring the unlikely stability of such a system) should approximately double the fraction of asteroids that hit the moon(s), reducing Earth's share of the impacts from 93% down to about 86%. (In fact it should be a little higher, about (93%)² ≈ 86.5%, to account for the fact that some of the asteroids hitting the second moon would've instead hit the first moon if the second one wasn't there.)
That's way more than a 0.001% reduction in impacts, but still less than a 10% reduction. So the protective effect of the second moon would be noticeable over geological timescales, but most of the asteroids on course to hit the Earth would still get through.
Neither effect is significant.
Asteroids hit the Earth because they happen to be on a collision course with the Earth. The Earth's gravity can deflect some that might just miss the Earth onto a collision, but this effect is not great. So asteroids don't hit the Earth because they have been attracted towards it by the combined gravity of the Earth and moon.
Now it is possible that some asteroids that would have hit the Earth hit the moon instead. But the moon only covers less than 0.001% of the sky, and so leaves us vulnerable to 99.999% of asteroids. A second moon might decrease this to 99.998%, but it's not going to be a big change.
So if we had had a second moon, the rate at which asteroids hit us would be almost exactly the same.
If the Earth had another it would have to be a very small moon that would wouldn’t really due any good about taking an asteroid impact it would probably be the same size or smaller than the impacting asteroid. Our planet current moon is actually to big for our planet and has been slowly but surely escaping our planets orbit. If we had another large moon in our orbit asteroid headed toward wouldn’t be our our concern. They gravity if the new moon would pull on our planet along with the old moon as well as them pulling on each other if it doesn’t cause a collision or sling shoots out of orbit into who know where it would most definitely cause gravitational friction that heat our Planet up and we would lakes and ocean of molten rock. As far as what we have discovered planet wise our planet is special in the fact that we have such a large moon for our planet and whatever event that may have happens for us to have our moon rarely happens but our solar system is the only place it has been observed. Planet similar to Earth any where if they have a moon they are small like mars