That whole "kills people while leaving buildings intact" line is a load of crap. A neutron weapon is still a nuclear bomb, complete with the attendant fireball and blast effects. It is just a much dirtier version of a standard nuclear weapon.
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Actually, just the opposite. It is a battlefield tactical weapon with a low yield blast that emits large doses of neutron energy on the target with minimal amounts of long lived fission byproducts. The idea is to kill people (and other living things) but not cause long term radioactivity at the blast site allowing troops to safely enter the area after a few days. If anything, it's a "clean" bomb. ;~(
See Neutron Bomb
Blast radius much smaller, overpressure quite limited. Whereas, a standard fission weapon is optimized for blast and overpressure (e.g. the neutron flux is inner directed and focussed at the core of the explosion) an enhanced radiation weapon is optimized for a longer, outward directed neutron flux. Less neutron flux into the fissile material means a less energetic explosive force. The energy goes into the neutron flux instead of a blast. Still, it would be a bummer to be closer than 1000 yards or so, assuming the neutrons would not fry you.