I looked it up, specifically here is the change:
It codifies many abortion rights laid out in Roe and other court rulings, including a provision permitting late-term abortions when a woman's health is endangered. The previous law, which was in conflict with Roe and other subsequent abortion rulings, only permitted abortions after 24 weeks of pregnancy if a woman's life was at risk.
https://www.usnews.com/news/best-states/new-york/articles/2019-01-22/ny-lawmakers-set-to-pass-bill-codifying-abortion-rightsAccording to that the main difference is they used to be permitted when the woman's life is in danger, now if the woman's health is in danger.
Sometimes I might agree with "health" reasons (very extreme cases) but mostly I fear we will end up using "psychological stress" as a "health reason".
I looked into the history of abortion. Surprisingly they were often perfectly legal all the way through the pregnancy however they were very dangerous to the mother. The first anti-abortion laws were enacted because
mothers were dying from the procedure and the laws were meant to save the women.
WARNING: GRAPHIC DETAILS DO NOT READ IF YOU ARE EASILY UPSET
The actual procedures for late abortion (dismemberment, crushing of the head and so on) are not at all new. I have an obstetrics book published in 1881 (wow my book is 138 years old!) that details the procedures and they have changed little since that time. The biggest difference is back then, before cesarean section became safe, usually they were done because the baby could not be normally expelled due to cephalopelvic disproportion (head too big for mom's pelvis, often due to maternal bone deformities caused by tuberculosis, malnutrition etc.) and the baby was going to die anyway if not already dead, or the baby was in an impossible lie such as transverse, which if labor has progressed and the baby has been pushed too deep into the pelvis it's spine is broken anyhow (it's been folded in two quite violently) and it is dead or dying but even if it's not, the mother would definitely die if the baby isn't gotten out somehow, and vaginal extraction was the only way to preserve the life of the mother back when cesareans usually killed the mother.
These were the situations where the doctor and possibly the father would have to decide whether to save the life of the mother or the baby and usually the mother won because she already had other small children to raise and her "worth" was far more to the family. You must remember back then there was a high mortality rate among children. You wouldn't save a baby that had a 50% chance of not surviving childhood anyway when you could save the mother who could live on and produce many more children for you as well as care for the ones already born.
So back then these procedures, including the infamous "partial birth" breech maneuver, were normally not done on a healthy mother and baby just to terminate a late pregnancy, but were used after labor had already started and could not complete for some reason, or were done when the baby had died in utero and labor was delayed too long putting the mother at risk for sepsis. Today they are still used in the latter case, babies still die from natural causes before they are born, and need to be gotten out. And in that case it's stupid to perform major abdominal surgery when a vaginal route is possible.
Nowadays abortion laws exist to protect the baby, not the mother. We have flip flopped our perception of value and now value the fetus's life above the well being of the mother (if having an unwanted baby stresses her or lowers her quality of life) and above the well being of the fetus's already born siblings (if additional children reduce resources available to the older siblings). Low child mortality means each child born is an entire human life and each abortion is erasing an entire human lifetime.
Family economics has flip flopped. One more child in the past added to the family's economic well being (another hand to work the farm) but today one more child depletes the family's economic well being - children do not contribute anymore; they are instead a huge financial drain. Hence a BIG incentive to abort them and I believe why abortion laws now exist to protect the fetus instead of the mother.
But in summary, I'm very concerned about this law. It's going to lead to "health" reasons little more than "I'll have stress and anxiety having to budget to raise this kid" and in MY moral world that is NO reason to kill my own baby.