DU isn't just used for anti-armor uses because it's heavy. Tungsten works for that. It's used because it combusts on impact at extremely high temperature. From wikipedia:
On impact with a hard target, such as an armoured vehicle, the nose of the rod fractures in such a way that it remains sharp. The impact and subsequent release of heat energy causes it to disintegrate to dust and burn when it reaches air because of its pyrophoric properties (compare to ferrocerium). When a DU penetrator reaches the interior of an armored vehicle, it catches fire, often igniting ammunition and fuel, killing the crew, and possibly causing the vehicle to explode.
Suspicion, not confirmed, is that the oxides and salts produced by this combustion would be carcinogenic or otherwise toxic if inhaled, where the relatively weak alpha decay would suddenly be hitting vulnerable lung tissue directly (in addition to chemical toxicity). But the jury is still out on the whole question of whether or not the dust actually stays aerosol long enough to be a real hazard, or settles into the soil in concentrations significant enough to be an issue.