Showing your own demo is a excellent idea. Before you do though, suggest probing for background details on their current websites, e.g. "just curious, how did

Showing your own demo is a excellent idea. Before you do though, suggest probing for background details on their current websites, e.g. "just curious, how did you decide upon the current format/template?" Take a consultative approach, "what works/doesn't work with what you have now?"