Be burned over a slow fire, or napalmed?

Die the death of a thousand cuts, or be decapitated?

Be hit with a shotgun blast, or a single bullet?

While somewhat artificial, these are the sorts of choices faced by the potential of a large impactor fragmenting into many small ones. For a variety of reasons it's probably best to take the hit in one place and let that one place be devastated than spread the damage.

There is a limited size range of impactor where this doesn't hold, and significant damage reduction can occur by fragmentation, but it's not well defined at present. A Tunguska-sized object has the potential to destroy a city but 100 fragments of one would simply be a blazing meteor shower. Certainly by the time you're ten or 100 times bigger than Tunguska you're playing dodgy odds - by fragmenting you increase the chance of at least one city hit.

On the other hand, if you can get really early intervention (years prior to impact) you could "easily" deflect the whole thing or fragment it into such a disperse cloud that the odds of any one piece hitting Earth would be low - that pass round the Solar System (but remember you've then built a whole population of Earth-crossing PHA's that you have to keep track of)