Mmmm, tricky.
Depends on the person I think. The MIL is sadly dead, so it makes no difference to her who is at her funeral. However, it may be something that the husband needs to do for himself, as a way of saying goodbye/closure etc and he wont get the chance to go to his mothers funeral again.
However, to welcome a new baby into the world is a wonderful thing, and some women really need the support of their DH. I would be terrified to go through the birth without DH with me.
Also, if I had died, I would be totally horrified that my son came to my funeral instead of supporting his wife. I would want him to focus on the future not the past.
My dad died when I was 18 and I thought the funeral was the most awful thing I had ever done. I said goodbye to my dad the night he died, I dont need a church to do it in. But thats my very personal view and I respect that not everybody feels the same.
But as somebody else mentioned, the chance of this happening must be very remote, as the funeral lasts 45 min or so. I suppose if you have to travel a distance to get to one or the other you could miss.
So if it came to the crunch, and the funeral was 3 hours away from the birth, I would say Birth.