The impact of a major asteroid hitting us would just be the begining of the problem. the immediate devastation would just be on a local level probably only a few hundred square miles.
The problem will be the huge amount of dust put into the atmosphere. We know that from just the one volcano of Krakatoa that suffieient dust was lifted to effectilvy reduce sunlight for 3 years. The first year was known as the year without a summer. There were no summer temperatures anywhere on earth the first year. It even snowed in the USA in July. the dust caused reduced temperatures for at least 3 years.
A large asteroid would change the climate for at least hundreds of years. It is these climatic changes that would alter the Earth. Reduced food production etc.