How to run a scan equivalent to nmap vulnerabilities scan

Question

I use Nmap for network reconnaissance but want to run a vulnerability scan equivalent to what tools like Nessus or OpenVAS provide. My questions are:

• Which Nmap scripts (NSE) are useful for vulnerability scanning?
• How to automate and filter relevant security findings.
• How to compare Nmap’s capabilities to dedicated vulnerability scanners.
  A detailed command-line example would be great.