Is white vinegar as effective against black mold as rice or apple vinegar?
The rationale for using vinegar in treating mold is that the acidity disrupts the pH balance that it needs for growth.  Black mold's growth range runs between a pH of 4 and 7.  Different vinegars will have different pH values that run between 2.4 and 3.4, so the vinegar with the lowest pH would presumably be the most effective (although lemon juice or a citric acid solution would be even better).  However - the other consideration is that upsetting the pH balance only slows (albeit pretty dramatically) fungal growth, so I'd actually go with a distilled vinegar personally - cider vinegars contain some solids and unconverted sugars that would potentially provide a food source.

Note that you can go the other way with pH and use a base instead of an acid. A saturated solution of baking soda in water will have a pH of somewhere around 8.1, so it should be effective via the same mechanism.

Finally, you can mix baking soda and vinegar and use that on molds instead, although this would not be using a pH vector - it would be using an oxidizer to disrupt growth.