My dear mother never got to meet my child. My dear MIL doesn't see him as often as she would like (not my fault - she was the one who moved across country), but she has a good relationship with him.
However, if my mum was still alive, and both grandmothers lived in the same city, I would probably spend twice as much time with my own mother as I would my MIL, just because she is my own mum, and I would want to see her, and she me. MIL would still see DS twice a month or so, but I would probably choose to see my own mother once a week.
That's normal. Seriously, it really isn't a competition. Any MIL who tries to make it one, is always going to lose.