It looks like I may have been too quick to judge that the civil partnerships that are currently available in the UK provide the same legal rights as marriage and that that is all that matters. From the comments I learned that this is not the case.
One difference, as I understand it, is that religious institutions are allowed to perform marriages but not allowed to perform civil unions. So a same sex marriage ceremony is legally prohibited from being performed by a member of the clergy even if he/she is willing to do it.
Another is that when couples go to another country, that country might not treat the partner as having the same rights as a spouse. For example, if someone with dual UK-US citizenship enters into a civil partnership in the UK, then when they come to the US, the partner is not eligible for permanent residency the way a spouse would be.
So clearly civil partnerships are still inferior to marriage in terms of legal status and privileges.
The second point raises the general question of how governments recognize the marriage laws of other countries. For example, according to the Koran, a man can have up to four wives and some countries legally allow this. Suppose such a person comes to the US with all his wives, does the US government give all the wives the same rights? According to this NPR story, the answer appears to be no, but some Muslim men in the US covertly marry more than one woman anyway.
Here’s how a man gets around the laws: He marries one woman under civil law, and then marries one, two or three others in religious ceremonies that are not recognized by the state. In other cases, men marry women in both America and abroad.
“Legally, they’re invisible,” says Julie Dinnerstein, a senior attorney for Sanctuary for Families. “If you are the second or third or fourth wife, that marital relationship is not going to be recognized for immigration purposes. It means if your husband is a citizen or green card holder, he can’t sponsor you. It means if your husband gets asylum, you don’t get asylum at the same time. The man is always going to be in a position of greater power.”
Apparently in some Muslim societies, being a second, third, or fourth wife confers much greater acceptance and social status on a woman than being a widow, and so women are willing to enter into it.