I think in terms of force:mass you can't beat nukes. We know how to make them, we know how to put them on rockets, and we can can line them up to detonate a lit

I think in terms of force:mass you can't beat nukes. We know how to make them, we know how to put them on rockets, and we can can line them up to detonate a little away from the asteroid, while a landing would need to match velocity. Probably the best would be nuclear shaped charges a la Project Casaba-Howitzer, which I believe were initially explored as a vehicle propellant.