Well this certainly ratchets up the discussion, eh? Massachusetts's federal lawsuit to overturn DOMA relies on a federalist argument while GLAD's case is based on equal protection claims.
The lawsuit questions the constitutionality of Section 3 of the law, which defines the word "marriage" for the purpose of federal law as "a legal union between one man and one woman as husband and wife." It does not challenge the constitutionality of Section 2, which provides that states are not required to recognize same-sex marriages performed in other states.
The suit alleges that the law violates the 10th Amendment to the Constitution, which reserves to the states all powers except those granted to the federal government. It also alleges that the law violates Article 1, Section 8 of the Constitution, which limits the power of Congress to attach conditions to the receipt of federal funds.