A nuke would emit lots of short wavelength radiation such as ultraviolet and x-rays. An asteroid would emit ordinary light and heat. The energy of a photon is supposedly inversely proportional to its wavelength, and the nuke would have a lot more high energy reactions. Although the total energy could be the same for a small nuke and a large asteroid, the distribution of energy in the spectrum would be different.
All true, but the nuclear detection satellite system is pretty much based on immediate visible light/flash detection for an immediate alert. Radiation effects and spectrum analysis comes after the initial alert (in some cases, well after). Not really a problem normally, but it could be a BIG problem in a tense situation. Like, for example, an atmospheric hit over Israel about 10 minutes after the bombs start landing in Baghdad.
We do need to get a better catalog of possible Earth-intersecting asteroids. This is not a major threat, but in the right circumstances it could be bad.
(Now, if we could just figure out how to redirect the asteroid INTO Baghdad...)