Confirming the earliest work, against the most recent one, we find that same-sex couples are more likely to break up than different-sex couples; the gap in stability is larger for couples with children

Stability Rates of Same-Sex Couples: With and Without Children. Doug Allen & Joseph Price. Marriage & Family Review, Volume 56, 2020 - Issue 1. https://doi.org/10.1080/01494929.2019.1630048

Abstract: In contrast to earlier studies, several recent ones have claimed that stability rates among same-sex couples are similar to those of different-sex couples. This article reexamines these latest accounts and provides new evidence regarding stability rates using three large, nationally representative datasets from the United States and Canada. Confirming the earliest work, we find that same-sex couples are more likely to break up than different-sex couples. We find that the gap in stability is larger for couples with children, the very group for which concerns about stability are the most important.

Keywords: Children, divorce, same-sex relationships, stability of relationships

Conclusion
We use three large, independent datasets to examine the relationship stability of same-sex couples, taking special note of couples with children. Although there may be some concern regarding the use of independent data, the fact that we find consistent results, while holding constant the same variables in three different legal environments and with data sets constructed in different ways, offers rather compelling evidence of robustness.

Dissolution rates of both same- and different-sex couples vary significantly across panels, in part due to how dissolution and same-sex was measured in each panel, and due to the length of time and time periods the data cover. However, the patterns in the results are strikingly similar. We find not only that same-sex couples are significantly more likely to dissolve their relationship than comparable different-sex couples, but also that this effect is larger for same-sex couples with children. This difference is statistically significant in almost all cases and suggests that parental instability is an important factor through which parents’ sexual orientation influences children’s outcomes. This channel may be the driving force behind recent findings of poorer child outcomes in same-sex families.

We do not want to overstate our results. We must be aware that same-sex couples make up a small fraction of couples in both Canada and in the United States, and that of those couples, only a small fraction have children present in the household. This is clearly a fact in our analysis where the fraction of same-sex couples is very small in each dataset. Furthermore, the definitions of same-sex couples vary across datasets, individuals may have changing incentives to self-report over time, and formally recognized same-sex unions are relatively new. This suggests that the reported number of same-sex unions is fluid and thus will continue to fluctuate. These considerations are also relevant, perhaps more so, for studies using small, biased samples.

However, in the case of relationship stability, the evidence seems quite consistent: same-sex unions appear less stable. This result was found in the first study of Andersson et al., but contrasts with some of the other studies that followed. Our findings therefore (like those of Wiik et al., 2012) reaffirm Andersson et al., and expand the literature by studying the difference between couples without children and couples with children.