As @phoog stated, a change in format does not matter as long as the certificate contains the required information, and is genuine. The only exception I've heard of is Puerto Rico birth certificates issued before July 1, 2010; Puerto Rico has required replacement of these due to security lapses with the older certificate.
Over the years states have offered certificates with varying amount of information, everything from every bit of information they have on file to a really short certificate. Sometimes the really short ones cost less than the longer ones.
The information the US State Department currently requires is
- Lists applicant’s full name, date of birth, and place of birth
- Lists parent(s)’ full names
- Has the signature of the city, county, or state registrar
- Has the date filed with registrar's office (must be within one year of birth)
- Has the seal of issuing authority
I don't know exactly what the State Department counts as a full name, but in the US, when dealing with state and local government, I have often been able to list just my first and last name when a form required a "full name".