In Britain, they do, by quite a margin. There's some fascinating and counter-intuitive data that back it up (it's not apples to apples since civil partnerships do not carry the social status of civil marriages, but it's not far off, since British CPs are identical in rights to CMs.) But this is a striking result:

The most recent evidence from the UK Office of National Statistics finds that homosexual couples that joined in 2005 were significantly less likely to have filed for dissolution four years later than heterosexual couples were to have filed for divorce: 2.5% compared to 5.5%. As Hattersley points out, however, male couples were much less likely to dissolve their relationship than were female couples: By the end of 2010, 1.6 % of male civil partnerships had ended in dissolution compared to 3.3 % of female partnerships.

This data may shift again over time. But who predicted that gay marriages would have lower divorce rates than straight marriages? Not me. And who predicted that gay men would last longer in marriage than lesbians? No one. So the one thing Jesus insisted on in marriage – no divorce – is now best upheld by gay male marriages. (Cut to Gary Bauer's head exploding.)

But why the higher lesbian number? Aren't women supposed to be the more stable of the genders? Marina Adshade airs many possible explanations, including this one:

[P]eople who have been divorced in the past are far more likely to divorce in the future. In the UK in 2010, 19% of male civil unions were between a previously single man and a previously married man while 27% of female civil unions were between a previously single woman and a previously married women. If lesbian women are more likely to have been in a heterosexual relationship in the past that ended in divorce (which appears to be true) than are gay men, then there is nothing surprising about their higher divorce rates in that gender group.

Obviously we need more studies to come to a better understanding, but Occam's razor points to this, it seems to me:

Women who want out of their heterosexual marriages file for divorce much sooner than do men who want out of their heterosexual marriages.