Would the Earth fare better if the Moon blocked the meteor, comet, rogue planet, or otherwise rather than a direct impact? At what point would the Moon's debris would be an extinction event?

The limit of the impactor is the size, angle of attack, or composition in which to moon would no longer be of any protection.

The Moon orbits the Earth from $approx$ 380000 km, but its radius is only $approx$ 3500 km. The sky has 41253 sq degrees, and the Moon covers only $approx$ 0.25 sq degree from it.

Thus, the probability that an incoming meteor is blocked by the Moon, is $approx$ 1:160000. Thus, the Moon is totally unfeasible to protect us from anything.

The debris would work like an "insurance": it will be more likely that some debris will finally end up on the Earth, but their summed damage will be likely negligible, compared to the meteor.

Note also, different meteors regularly cross the orbit of the Moon, but they have still a very small probability to hit us.

It would be much better for Earth if the impactor hit the moon...

In this Worldbuilding answer, I used a paper on ejecta kinematics to do calculations for ejecta velocity upon impact. Without going into too much detail here, much of the ejecta from a large impactor would not exceed the moon's escape velocity of 2.38 km/s. You can examine Figure 7 from the linked paper which shows the logarithmic relationship between ejecta velocity and the edge of the crater. Only material within a few tens of meters of the edge of the formed crater can attain the velocity needed to escape the Moon's gravity.

The mass of the asteroid increases with the cube of its radius; while the mass of material within $n$ meters of the edge of the impact crater increases with radius; so it is evident that the the larger the meteor itself gets, the lower the danger of the any potential ejecta relative to the original impactor.

Furthermore, material ejected from the Moon has the potential to land back on the Moon, enter a stable orbit of Earth, or be ejected from the Earth-Moon system; so only a (probably small) fraction of Moon ejecta would threaten Earth.

Overall, fewer, smaller rocks are much better than large rocks when it comes to getting hit by things (except maybe for your car's windshield).

...unless the impactor knocked the Moon into Earth.

Of course, there is always the possibility that a very, very large impactor would knock the moon into a different orbit, potentially one that eventually impacts Earth. That would, obviously, be the worst case scenario. Significant changes to the orbit of the moon, even if these changes do not cause a collision with Earth, have the potential to do significant damage in terms of tides; not just ocean tides but also the poorly understood effect of tidal forces on Earth's mantle.

In any case; it is probably much better for a large impactor to hit the Moon instead of the Earth, but possibly much, much worse.

A meteor is a small, sand grain or pea-sized fragment which burns up in the atmosphere before hitting the ground. Those large enough to reach the ground ae called meteorites. It seems to me the ones you are talking about are large enough to be called asteroids. The moon affords hardly any protection against asteroids, and those that strike the moon do very occasionally cause tektites (small glassy beads) and small pieces of debris to hit the Earth. The next asteroid on a collision course for Earth is most unlikely to be blocked by the moon, but there's no need to worry. Chelyabinsk or Tunguska events are fairly common and occur several times a century, usually striking the sea, but the really big ones like Manicouagan or Chicxulub occur on average about once every 150 - 200 million years. We will probably have already become extinct by the time the next one hits.