From what I see, I would rather use it to describe a grow-up person who is smart, well-educated and experienced. Complex and complicated more refer to things and stuff. So base on what I say, you could use them like this: a sophisticated man a complicated/complex situation a complex/complicated device

Sophisticated ( adj ) means advanced ..... having or showing signs of experience in social life and behaviour Unsophiticated means : not easily understood ; complicated . wow this machine is sophisticated

I would typically use this word for expressing the idea that a device/machinery/engine is a complex one (uses advanced technology) : a sophisticated clock, a sophisticated rocket. Additionally, I think that it's also possible to use the word in the context of fashion : that woman has a "sophisticated" hairstyle .