Both documents serve to protect children lawfully from situations that could hard their development. While the 1959 Declaration does a decent job of acknowledging what this might specifically entail (ex. entitled to education, name and nationality, social security, protection against practices that would foster neglect etc.) the Convention of the Rights of the Child (UNCRC) goes into more depth about what this all could really mean. This revised document serves to protect the child in a more lawful manner as it is more specific about how exactly the child should be protected.
Some notable differences between the two documents are the pronouns being used pertaining to gender. In the 1959 Declaration the child is only referred to as male with he/him pronouns. However, the UNCRC is careful to make sure that the document is written with a more gender neutral manner. Additionally, the UNCRC defines what it means to be a child while the 1959 Declaration does not.