The Defence of Marriage Act has three sections, the first lays out the reasons for the act, the second exempts same-sex marriage from the requirements of the full faith and credit clause (note that recognition of marriage is not required under that clause anyway and so it effectively does nothing), and the third defines marriage as one man and one woman for purposes of federal law.
I see section 3 of DOMA as a theft of responsibility from the states, which generally otherwise get a free hand in defining family law for their residents. Once marriage is made into a federal issue then the federal government can steer the states on the matter. The DOMA is itself not too threatening in this regard since it is only one criteria added. However, if in the future, other criteria are added, navigating the state and federal marriage codes could become quite complicated and states would have every incentive just to incorporate federal law by reference, thus depriving states of sovereignty in this area.
To be sure DOMA could be struck down in a very bad way, in a way depriving the states of their sovereignty in this issue. I don't think think that will happen because I don't think the court will want to dive into such a contentious issue right now and upset so many state's laws, and so any victory against DOMA which is in line with a court.
Some things, such as eligibility to marry, should be between a state and her people, not between the federal government and the people. The size and scale of social machinery are the principle threat to family and tradition and for this reason whatever the federal government is capable and competent to defend, marriage is not on that list.