First figure out if anyone has other plans that day. Then consider what the event is. Who else will be at tthe event. Do more than one (or ANY) of your partners WANT to go. Consider all the practical things first, and if you still have to decide, all other things being equal, then flip a coin and take turns.
Recently my Spouse earned a certificate of achievement from the Appalachian Mountain Club, and they have a little "awards banquet" type of thingy where they congratulate people and hand out the "diplomas". Spouse's other partner "invited theirself" to this, and bought a ticket, and then something else came up and they decided they "couldn't" go. They wrote to me on FB asking me if I would like to go. I said "oh how cute, my spouse's other partner trying to set us up on a date, LOL" (and they thought I was offended at first). Turns out, I already had plans for that date and all 3 of us ended up doing separate things. The extra ticket was only $10 or so, so it wasn't that big of a deal.
I guess my point here is twofold - 1) just because you have more than one partner, it doesn't mean ANY of them have to or will be available to be your "date". 2) if you feel that choosing one person because the invitation says "+1" implies a value-judgment about the relationships, you could always opt out of bringing a guest, or you could invite a guest who is a friend instead of a partner.