These two adjectives have different meanings, though they are closely related; both refer to superior powers of observation and understanding. Per-spic comes from roots meaning “to see through.”
Perspicacious describes a person who has sharp insights and clear understandings, or the insights themselves:
The PhD student was perspicacious; she had perspicacious insights into physics.
Perspicuous describes ideas or words that can be clearly understood:
Samantha wrote a perspicuous dissertation on quantum theory that influenced many people.