Compare and contrast Piaget and Vygotsky's views on the stages of development?
This question is a little difficult to answer since Vygotsky doesn't really have "stages" like Piaget does in his theory.
The developmental theories of Piaget and Vygotsky are not only different in nature, but different in approach, and you are right in that they are difficult to compare. The best way to approach the comparison is to look at overarching principles, rather than the little details.
The biggest difference between Piaget and Vygotsky was in their assessment of a child's progression of development. Piaget believed that babies are born completely "ego-centric" and development proceeds from the individual first, and moves outwardly. (Evidence of this might be suggested by the time it takes for a baby to recognize its mother vs recognition of its own hand.) Piaget also believed that physical development (and hitting physical milestones) preceded internalization (learning, mental understanding). Essentially, Piaget believed that learning and development begin as a type of survival instinct, and the child grows to understand that other people can be part of this process.
Vygotsky, on the other hand, believed development begins on a social level (through social interaction) and is gradually internalized, or made personal. Vygotsky believed learning precedes development (exactly opposite to Piaget), meaning, a new stage of development is not reached until the child has internalized the idea or lesson.
Both theorists agree that development can be the result of "cognitive conflict." In other words, both agree that when children experience a moment of difference between what they believe and what they actually perceive, they will figure out a way to bring about balance (Piaget called it "adaptation" and "assimilation"; Vygotsky uses the term "scaffolding" or using prior knowledge to understand something new).