Grandchildren – and I have six of them, ranging from three to 16 – are a joy, a delight, a pain in the neck and a worry that keeps you awake all night. What happens before and immediately after the first one is born doesn't have to set the pattern for the rest of their lives or the rest of ours. Cots, prams, clothes, toys, etc. are things and, of course, it is nice to help your daughter/son with the staggering costs of a newborn baby. It is not a competition and anyone in the family who makes it so is being unutterably silly and no one else in the family should take any notice.
What any sensible parent wants from their child's grandparents is love, time, care and thoughtfulness; they may not fully realise this before the child makes an appearance.
What I have found as a grandparent is that I am the only one in the family who has the time and patience to mix paints and provide huge sheets of paper for painting. I am the only one who has the time to play endless games of snakes and ladders, Dodge the Dino, Ludo, backgammon, Lunch Box, Hungry Dinosaurs, go fish, the Captain's Mistress, etc. and read the same story to the three-year-old eight times on the trot. That is not because my son-in-law's parents are uncaring – far from it as they are wonderfully loving but just live further away and cannot see the children on a daily or even weekly basis. As far as I know they are not jealous of the time (quite a lot) that the grandchildren spend with me and nor am I jealous of how the grandchildren rave about the magically wonderful time they have had when they have visited Grandma and Grandad.
Being a grandparent is something we do for the rest of our lives. It would be wise to do it informed by love and an ability to keep the lip zipped about "it wasn't like that in my day". It would be silly to compete with the "other" grandparents because it is something they will also do for the rest of their lives.
I am fortunate in that I get on very well with the other grandparents, although we don't see each other very often. However, if we didn't get on, I would a) continue to be polite and b) take no notice of anything derogatory about me.