The uranium miners did suffer high rates of lung cancer, but it was due to primarily to radon gas.  Unlike DU, natural uranium is found in conjunction with its decay products, which include radium, thorium and radon.  The "radon daughters" are potent source of internal alpha radiation if inhaled because they have half-lives measured in minutes, seconds and less.

I think that the last comment was basically correct in that the chemical toxicity of DU is a primary concern.  This toxicity should differ little from the chemical toxicity of natural uranium (the isotopic state being irrelevant to chemistry).  There are a number of reviews of uranium toxicity, including one that I wrote and could provide off-line to anyone who is interested.  But the main health concerns in my opinion are kidney damage, birth defects and chromosomal aberrations.  There is more limited evidence of some other effects.

The radiation from DU should not be entirely dismissed, however, as a concern, for at least two reasons.  One, there are huge quantities of DU in some of the military vehicles and munitions.  Two, once internalized, as would be the case after breathing smoke and fumes from a detonation or as an embedded fragment left in the body, the alpha particles are highly effective at causing damage to DNA.  There is a need for more research on the problem.