Two advanced security features available on the Cisco SD-WAN WAN Edge (vEdge) device are the Enterprise Firewall and URL Filtering. The Enterprise Firewall provides robust protection by inspecting and filtering traffic based on defined security policies. URL Filtering helps in blocking access to malicious or inappropriate websites, thus enhancing security. While features like Cisco AMP and Cisco Umbrella DNS Security are advanced, they are not specifically noted as inherent security features of the vEdge device.