Well, this isn't exactly the same situation but it's similar. My step-son's birthday is on Christmas Day. Talk about competition!
We've always celebrated birthdays with family at dinner, letting the birthday child pick the dinner and type/theme of cake. This worked well for us because we celebrate Christmas in the morning. Perhaps you could split the day so they each have their own special party time.
Another tradition we have is the "Birthday Fairy" paying a visit during the night, leaving ballons and 3 small gifts to ward of the "birthday gimmies" for the majority of the day. We did this with each of our 6 kids up through their 12th birthdays.
Parties with friends were on the most convenient weekend. Our kids never had a problem with this, probably because it added another party!
We asked my stepson if he'd prefer celebrating his birthday on a different day, or even a different month but he preferred sticking to his own day. :-)
Costs add up quickly when you're celebrating birthdays together (and a birthday with Christmas). We always save throughout the year so we can spend as much on the Christmas birthday boy as we spend on all the other kids' birthdays and still afford family gifts at holiday time.
Happy Birthdays!