Joe,
Kinetic kill vs nuclear weapon was very heavily studied by LLNL back in the 1990s.
The nuclear weapon can deliver orders of magnitude more energy than can a kinetic kill.
The idea is we want to change the orbit of the asteroid, and that takes energy. If the asteroid is large, we have no way with our chemical rockets to put enough energy into a kinetic kill vehicle to be able to deflect a very large asteroid.
Again, for very large asteroids, or very short time for deflection; the nuclear weapon is the ONLY viable option. It beats kinetic impactors, "gravity tractors"... hands down.
One of the other problems with kinetic kill is that many of the asteroids are what are called "rubble piles". They are not one rock, but a bunch of rocks held loosely together by mutual gravity. A kinetic kill will deflect the rock it hits in a rubble plie, but won't deflect the bulk of the others. The only force between the impacted rock and some of the others is gravity, and gravity is too weak for the short time scale to impart enough momentum.
Dr. Gregory Greenman