The right to make a citizen. Civil union doesn't recognize this. My sister married a guy from the US, she lives and works there, after they lived for a few years in France when they first married 13 years ago. Though they underwent annoying administrative procedures in both countries to get the needed papers to live there, they have a stable situation and they may even choose where they want to live. They have no children, by the way, which doesn't jeopardize their situation.
One of my friends and possible house mate is from South America (he might move in, but financial/ family situation makes it seem unlikely, but well, this is another issue). Regardless of the nature of the relationship (we're friends, not committed lovers), it's not even theoretically possible to envision a long-term relationship. The civil union we have here won't give me the same rights my sister has.
Of course, a broader, non-partisan coalition to gain anti-discrimation laws could be a plus for all US citizens. They exist at state levels, when I was a TA in Iowa we used the Iowa Civil Rights Act to get full health insurance coverage for same-sex partners.