Assuming you are using the same VPN in both places, the security is the same from a confidentiality standpoint. Using a frame-relay system, you may gain some availability assurance, as even a VPN could be subject to a denial-of-service attack, which would be more likely on the Internet. On the other hand, the Internet may give you more alternate routes and thus better availability than a frame-relay network. Given that you will be using a VPN, there are probably reasons other than security that will determine your choice between frame relay and the Internet.
For more information on this topic, visit these other SearchSecurity resources:
Chat Transcript: Security and quality-of-service issues for virtual private networks
The Information Architect: The reality of virutal private networks
Best Web Links: Infrastructure and Network Security
This was first published in June 2002