Diana Baumrind, a psychologist known for her work on parenting research, identified different categories of parenting styles.
The restrictive approach you describe sounds very much like her "authoritarian" style of parenting. From the wikipedia article (note that I find the article to be rather biased in tone, and it cites a number of claims based upon speculative correlation, so I am only including specific edited clips):
Authoritarian parenting, also called strict parenting, is characterized by high expectations of conformity and compliance to parental rules and directions, while allowing little open dialogue between parent and child. Authoritarian parenting is a restrictive, punitive parenting style in which parents make their children to follow their directions and to respect their work and effort. ...
...Children resulting from this type of parenting may have less social competence because the parent generally tells the child what to do instead of allowing the child to choose by him or herself.
The other extreme, which you describe as granting freedom to the child, sounds like Baumrind's "Indulgent parenting" style:
Indulgent parenting, also called permissive, nondirective or lenient, is characterized as having few behavioral expectations for the child. "Indulgent parenting is a style of parenting in which parents are very involved with their children but place few demands or controls on them." Parents are nurturing and accepting, and are very responsive to the child's needs and wishes.
...in the better cases they are emotionally secure, independent and are willing to learn and accept defeat. They mature quickly and are able to live life without the help of someone else.
There is, however, a middle ground between the two extremes. Baumrind referred to this as "Authoritative parenting" (emphasis mine):
Authoritative parenting, also called 'assertive democratic' or 'balanced' parenting, is characterized by a child-centered approach that holds high expectations of maturity. Authoritative parents can understand how their children are feeling and teach them how to regulate feelings. They often help their children to find appropriate outlets to solve problems. Authoritative parents encourage children to be independent but still places controls and limits on their actions. Extensive verbal give-and-take is not refused, and parents try to be warm and nurturant toward the child. Authoritative parents are not usually as controlling as authoritarian parents, allowing the child to explore more freely, thus having them make their own decisions based upon their own reasoning. Often, authoritative parents produce children who are more independent and self-reliant. An authoritative parenting style mainly results when there is high parental responsiveness and high parental demands.
Authoritative parents will set clear standards for their children, monitor the limits that they set, and also allow children to develop autonomy. They also expect mature, independent, and age-appropriate behavior of children. Punishments for misbehavior are measured and consistent, not arbitrary or violent. Authoritative parents set limits and demand maturity, but when punishing a child, the parent will explain his or her motive for their punishment. They are attentive to their children’s needs and concerns, and will typically forgive and teach instead of punishing if a child falls short. This is supposed to result in children having a higher self esteem and independence because of the give-take nature of the authoritative parenting style.