In what case should I use a PKI to conduct my transactions? And in what case a VPN?
You've set up a false dichotomy. Virtual private networks (VPNs) can make use of public key infrastructure (PKI). You use PKI whenever you want to tie events or transactions to an individual. You use PKI when you need to use public key cryptography for more than just session encryption. VPNs may use PKI. Public Key Crypto may also. But they need not.
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It is not quite apples and oranges. It is more like apples and tomatoes.
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