The framing of your question is very problematic because it is a binary choice on something that is vastly too complex.
Monogamy itself is mostly a social construct built around oppressing women and treating them like property. In most cultures for most of human history men have been allowed, encouraged, celebrated as dogs and women have been traded like property and their vaginas treated like the gateway to legitimate property ownership. For gay relationships, mapping monogamy onto them is problematic in many ways, not the least of which is because that same set of cultural biases are unfriendly to anything other than "traditional" opposite sex activities.
Most importantly, biology has definitively proven that human bodies are not designed for monogamy. The penis is shaped to scrape out another dude's jizz and deposit yours deeper. Men ejaculate more when their brains think their partner has been having sex with others. And lots more. And biology will always beat cultural pressures, 100% of the time, eventually.
I would strongly encourage you, if this topic is of interest, to read a few things.
First, Esther Perel wrote a great book called Mating in Captivity that explores the cultural and biological underpinnings of monogamy. She did a lecture with sex advice columnist Dan Savage which you can hear here:
https://overcast.fm/+GeYbxRhmo/45:45
An excerpt:
Savage: Meg Barker writes that the pressure to perfectly execute monogamy over the lifetime of a marriage, half a century or more, makes every monogamous relationship a disaster waiting to happen. [...] Monogamy is the only standard for success. You did it perfectly or you are terrible at it. I get in trouble for telling people that if you're with someone for 50 years and they only cheated on you once or twice or three times, they were good at monogamy, not bad at monogamy.
Perel: For most of history, monogamy had nothing to do with love, and was primarily an imposition on women. Monogamy has never been an equal gender proposition. Men practically have a license to cheat, they have a whole series of theories that justify why they are natural roamers. Women were created as a domestic creature that never wants to go anywhere -- and I don't understand why she gets locked up everywhere if she never wants to go anywhere, but that's another thing. Monogamy was basically an economic imposition in order to know whose children are and who gets the cows when I die. It's about patrimony and lineage.
Then it was one person for life. Then it moved to one person at a time. A woman told me: "I was monogamous in my two marriages and with my three boyfriends since." I am monogamous in all my relationships.
Savage: Serial monogamy.
Perel: The concept changed, that it's one person at a time, not one person for life. When we used to marry and have sex for the first time, monogamy meant one thing. But today you marry and stop having sex with others, monogamy means something else. Exclusivity, coming after 10 years of sexual nomadism is very different from exclusivity that comes from coming as a virgin to marriage and then having your first and only experience for life. These terms are fluid.
Second, there was a great piece in the NY Times about 10 years ago looking at how important non-monogamy has been to actually maintaining and preserving many marriages. "Companionate" relationships have been a thing for thousands of years and are just as valid and certainly more fulfilling than decades long marriages that are "monogamous" yet only held together by hatred and resentment and cultural pressures. Check out:
Married, With Infidelities (Published 2011)