If you are expecting your first child, you have no way of truly knowing what to expect. Turning to your mother for advice and "been there, done that" stories can be very comforting and the closest thing to real knowledge you may have. But if your mother had the labor from hell that took three days, don't think you are "sentenced" to the same. And, if your mother had one of those births where she had no idea the baby was about to come until she started pushing, don't think you will have an easy delivery too.
The course of labor and delivery depends on many factors. Here are just some of them:The position of the baby at the time of labor. Whether you have a singleton, or are expecting twins. The size of your baby. Your birth setting, and whether you feel psychologically at ease or not. The availability of pain relief and medication to speed up labor if needed. How many babies you have already delivered. The way your body is shaped, and any medical conditions (like gestational diabetes) you may have.
Only the last one really has any connection to your mother. I know one woman who had a cesarean section due to a genuinely tiny pelvis. Her mother, who has the same condition, also had to have c-sections with her babies. In other words, your mother's history of giving birth may be relevant to you if there are specific medical concerns. Otherwise, there are really no rules to go by.