Is there any advantage to being a veteran-owned business?

Yes! There are plenty advantages to being a VOSB (veteran-owned small business), especially in the government contracting space. According to the SBA, the federal government awards an annual portion (~3%) of its contracting spending dollars to veteran-owned businesses. These programs help VOSB's access these contracts. 

https://federalgovernment.info/vosb-government-contracting-with-fedcon