The term "VPN" seems to be causing problems here.
VPN is any network that is shared. That can mean a Frame Relay VPN, L2TP over Internet VPN, MPLS VPN, ATM VPN... but not "IPSec VPN" since IPSec provides encryption, not connectivity.
The original post asks which is better: Frame Relay or "VPN". The answer is "Frame Relay IS a VPN technology."
If you mean Frame Relay vs. an Internet-based VPN, then Internet-based is cheaper... or is it? By the time you add the cost of researching, testing, deploying and supporting IPSec/L2TP gear...
Frame Relay VPNs are more reliable, predicable and supportable. As are MPLS-based VPNs, ATM VPNs, etc...
Feel free to contact me by email if you'd like more detail.
Cheers!
Darin
email@darinhamilton.com