it largely comes down to mass, what type of asteroid(pebble heep or a solid chunk) it is and to a lesser extent heating of the atmosphere. If spoted early, a small nudge that you can impart with a nuke might be enough to kick it out of a collision course, at the risk that it also shatters. if spotted to late, its better for a single large asteroid to hit, that 1000 smaller ones, as all those smaller ones will heat up on atmospheric entry; super heating it and causing wider spread devastation/fires. An alternative way to think of it is like a gun, at close range would you rather take a pistol round, or a shotgun?
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