A number of studies have been done (on straight people of course) but I don't know why they wouldn't mostly apply to Gay people. The argument always comes up that "marriage is just a piece of paper." This ignores the fact that most people see marriage as a permanent thing and plan accordingly. They generally intertwine themselves in a joint checking, joint savings, mortgage in both their names, children etc. Society blesses the union with a religious ceremony. Part of the attractiveness of living together is that it can be dissolved without a word, if one of the parties is of the mind to be so inconsiderate. Just move out. But more on living together….Each party keeps their own money, often spending it in ways which would likely not occur in the married/mortgage/save for the children's colllege fund scenario. For (stereotyped example) the nonmarried man can gamble on the horses to excess and the nonmarried woman can spend as much as she likes on clothes. As long as each comes up with their half of the rent, who can chastise the other? Living together is just a completely different mindset. In the married model, it forsees the road may be rough, people blow up, lose patience, but marriage gives them cause to 'give it one more shot' since dissolving is much more expensive and painful, emotionally, socially etc.
Of course there are always exceptions; some can live together in a committed state of unmarriedness and vice versa, but in general this makes sense to me.
Interestingly, in the documentary "Saving Marriage" - the married (Gay) couples gave many of the same arguments I've summarized above!