I think there's more of a thought process for me. First in figuring out if it's a "want v want" conflict, "need v need", or "want v need". There's also more thought about how much I can actually do to meet this want or need, and how much responsibility I have to meet it. Since I live with MC, have joint finances, kids, house, etc I do have more responsibilities to him, and sometimes that does mean that I unfortunately have to put TGIB's wants second.
However, on the other side of the idea that living with MC means I have more responsibilities to him, is the thought that MC gets wants and needs met by me on a daily basis, so when there is a conflict I'm actually more likely to try to put TGIB first if I can. Since he is long-distance he already has to miss out on a lot of things.
So far there haven't been any major "need v need" conflicts. It helps that they're both very supportive of my relationship with the other and they're both very reasonable about the limits of my time. For instance, TGIB is coming to visit at the end of this week, for two weeks (YAY!). Usually, when he's here, MC is perfectly understanding about the fact that I will spend the majority of my time (including nights) with TGIB, since I so rarely get to see him. However, this time MC's been sick, I'm at that time of the month, and TGIB's going to be here for two whole weeks so we'll have other time available later, so I've already talked to TGIB about the possibility that MC may need a little more "me" time in those first few days TGIB's here. And TGIB was fine with it, because he knew I wouldn't be neglecting him to put MC first, I would just be putting the balance a little more towards MC than I usually do during TGIB's visits.
MC and I have kids together, and TGIB has kids with his ex, so I think we're all used to putting another's needs before our own. And ultimately, while TGIB and I do not plan on ever having kids together, once the long-distance part ends he'll be more of a co-primary. I definitely think my situation is made easier by the fact that MC and TGIB not only know each other, but are friends with each other. There isn't a "me vs him" mentality, instead we're all trying to do what's best for all three of us, which is probably why conflicts are limited. I'm as likely to have my wants and needs conflicting with theirs as they are with each other.
Pan Female, Hinge in a V between my mono (straight) husband, Monochrome and my poly (pan) partner, ThatGuyInBlack