Distillation can lead to impurities. DI water is usually more pure- because anything with higher volatility than H2O will go with the water vapor. Both are as pure as you're liable to be able to tell for home use. Pure water is an incredible solvent- until it's found enough crap to balance it out. It also has a low pH, think acid. That's why your tap water has hardness- it's leached out of the rocks it floats through/over. Concrete floors in a DI plant would be a tasty way to 'quench the hunger.' Metals will too, but not nearly as quick.De-ionized water is just that, isn't it--water without dissolved ions (eg iron, copper, etc etc)--the water itself is unchanged. You could call distilled water an extreme version of de-ionized water. It isn't more reactive or more of a solvent than any other form of water, it just has fewer "impurities" that could spot or leave deposits.
I'd agree with PFWiz, except- there are plenty of leftover impurities on the car's surface and in the air that will negate negate the purity. Soap will tend to buffer the water as well, so probably not a huge deal on the corrosion side.
From a cost perspective, if your water is fairly hard (50+ ppm), you're better off with a whole house Softener, then an RO to pull the rest. Way cheaper in the long run, and adds life to your water heater. One caveat- if your house has a soft water loop built in, the exterior bibs are probably NOT included as softened water tends to burn plants.