I would bring to gifts.
In this situation, we only gave a gift to our niece, not her friend who we didn't know. My niece had a lot of family members present, and her friend didn't, so there was a pretty big disparity in the number of gifts, and they opened them at the party anyway.
It's their choice to have a joint birthday party - I'm only attending in honour of my niece, so only one gift.
I think this is a good point. A joint birthday party shouldn't be seen as an opportunity for an "unpopular" child to get more gifts, from the near-strangers who are attending for the sake of the "popular" child (to put it in an extreme way). So I would focus my gift-giving efforts on the child I knew, especially since gifts won't be opened and totaled up in front of everyone.
I guess it does make some difference to me who is hosting the party, though. If Jason's parents (the unknowns) are hosting the entire party at their horse ranch so all the kids can ride ponies, I would be more inclined to get something for Jason, as a sort of hostess-gift-by-proxy. After all, my kid wouldn't get to ride a pony if Jason's parents hadn't agreed to host Charlie's friends as well as their son's. So in that case I'd probably get him a card and a "nice token" gift.
The bolded just makes me sad. How about using this as an opportunity to meet a new friend and extend you and your child's social network, rather than making a statement about who you like better?
On the other hand, if I had a child invited to a relative's birthday party and it was a joint party with another kid, I don't know that I'd be comfortable buying a complete stranger a gift. I went to cousin's birthday parties because we lived in the same large city, but I lived far enough away that expanding my social network was a ridiculous idea. My parents were willing to drive an hour one direction once a year for a birthday party, not for regular playdates. There was no reason to expand anyone's social network.
Yes, that's not the case in the OP, but in the OP it's not a case of who you like better from two known children. The OP said that she doesn't know one of these boys at all, neither do her children. In that case, of COURSE the OP and her kids like one of them "better" at this point, because accepting an invitation implies some level of liking the birthday boy, and any level of like is higher than a null value.
I vote one gift to the boy the OP and children know. Especially if they're not going to be opening gifts at the party.