A recent court case has clarified this issue and has said that for the VA, the Veterans Benefit Act takes precedence over the JWOD Act, and that contracting officers in the VA must first look for SDVOSBs and VOSBs to satisfy their requirements, before looking to AbilityOne, The VA has apparently created new procedures to follow that rule, which were ignored in this case.
Here's some information on it:
The Veterans Benefits Act is a specific mandate to the specific agency to grant first priority to SDVOSB and VOSB concerns in the awarding of contracts. The Javits-Wagner O'Day Act, on the other hand, is a more general procurement statute; were there a direct conflict between the two, the more specific Veterans Benefits Act would control. The court found that the agency was reasonable in concluding in its new guidelines that the Veterans Benefits Act should have priority. It therefore found that the contracting officer's actions in contravention of the new guidelines lacked a rational basis; there was no reasonable explanation for why she failed to consider them.
The COFC case is: Angelica Textiles v. The United States (10/26/2010).