It will be the higher deductible. The deductible is going up because the addition of the child to the plan/coverage right? So if you want any of baby's bills in the hospital to be covered, (which they will be assuming you do go an add baby within the month) then the effective date of baby's coverage will be retroactive to the birth even if you wait the full month to add him or her. So since the coverage will be retroactive so will be the new deductible/OOP max. This is better than the alternative which is that baby's bills not be covered at all during the hospital stay.
I remember one of the things that most surprised me as a new first time mom was getting the hospital bills for my child who was only weeks old. I was like - "No, this child is (still) an extension of me..Not a billable person!" It was just strange to me that this being that had been a part of my body was now getting massive bills in her own name at our address. And we had no complications - delivery or healthwise and we did have insurance..but due to the lag on the insurance coverage from needing to add her..I saw a lot of what we would have paid and it was CRAZY. We were billed for her pediatric checks, bathing, nursery time, immunizations, bedding, socks, take-home care package (thermometer, guaze, a few diapers, wipes, etc..).
To be even clearer - none of the care your baby receives will be covered/billed under your care. It's not a package deal As soon as your baby comes out of your body - the baby will be treated/billed as a separate person.