Birth Certificate/Passport have different dates

[JoeyKeano 21]

Ok, so here's my problem.

My last 3 passports show a different date of birth, to that shown on my birth certificate.

My passport shows it as 5th June 1985

My birth certificate shows it as 5th July 1985

I have already visited the USA 3 times this year, and when filling out the ESTA I put the date of birth as shown in my passport. This is obviously going to cause problems when it comes to filing for my visa.

I've sent off for a new birth certificate, with the dates changed to match my passport. If they send me that, will I have more problems when it comes to retrieving medical records/police records etc?

Or should I send off for my passport to be changed (a more expensive option, short term). In which case I'm worried that I'll be questioned why I travelled on an incorrect passport/ESTA.

I should note that my mother attempted to change my passport twice when I was a kid, sending my passport, birth certificate and a letter stating that they had made a mistake. Both times the passport was sent back, unaltered.