Maybe not. According to this:
In the UK, same sex couples can form legally recognized relationships, akin to marriages, and have had this right since the Civil Partnership Act came into effect in December 2005. Just like marriages these unions can be dissolved via a legal process similar to a divorce (which in the UK requires someone to be at fault).
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.As you can see from both the article itself and the comments, everyone with an opinion proposes reasons — some backed by evidence, some not — for the different rates. Most amusingly, one commenter writes,
It is very clear from the social research that men like being taken care of, and do get taken care of in het relationships more than women. Women do more of the work. I suspect gay men are also in it for getting taken care of (what you are oversimplifying as "stability."That comment makes gay male relationships sound like an Escher print.