Precious and valuable are synonyms so the meaning is pretty close. Although there is some opportunity for a difference in meaning as the word valuable tends to be used to describe something that has monetary value, whereas the word precious is sometimes used to describe something that is important but doesn't necessarily have any monetary value.

Building on that answer here are examples: My diamond ring is really valuable. It is also precious because it is one of a kind and can’t be replaced. My diamond ring is really precious because it used to be my grandmother’s. My relationship with my new business partner is very valuable. My relationship with my new grandson is precious. So precious implies emotional attachment or something irreplaceable.