Some cultures might find comparing items or people as lesser versions offensive. Use with caution. Be mindful when saying his artwork is the poor man's Picasso.
Pro Tip 2/3
Literal Substitute
It's often used to describe something fulfilling a similar role but with less prestige or quality. This shared office space is the poor man's private studio.
Pro Tip 3/3
Humor or Sarcasm
The phrase can be humorous or sarcastic, depending on context and tone of voice. Calling his bike the poor man's sports car got a good laugh.