When I was growing up, I lived within walking distance of my paternal grandparents. My brother and I were their only grandchildren, we saw them daily and were thoroughly spoilt by 'Big' Nanny, granddad was more remote and 'old school'.
My maternal grandparents lived a few miles away but in rural Norfolk in the 1950's we only saw them on high days and holidays as we had no car and the buses were infrequent. They had another 4 older grandchildren who lived closer to them. When we did see them, my 'Little' Nanny appeared to be straight-laced and less loving. Because the money had to go further, there were few treats for us. As a result when I was younger I much preferred my 'Big' Nanny. However when we got older and were able to see 'Little' Nanny more I learned to appreciate her kindness, sense of humour and intelligence. Where 'Big' Nanny could be difficult at times with other adults and hurt my brother by saying she didn't like boys past the age of 12, 'Little' Nanny had greater emotional intelligence.
BTW 'Big' and 'Little' referred to their height!
What I'm trying to say, is be yourself, your grandchildren will come to understand and love you in their own time. It isn't a competition, although both my grandmothers have been dead a long time, I remember them both and the time I spent with them with great fondness.
Now I'm a 'Nanna' myself, I try to remember the lessons I learned from both these wonderful women