The protocol proposed there has several shortcomings. Firstly, it assumes that merchant's web server would not be compromised. Mike Hearn said that the server needs to have access to SSL private key, so if it is compromised, the game is over. However, this is not true: SSL termination can be performed on a machine different from the one running the web server. Even if it is done on the same machine, web applications are typically run with limited permissions, so they can't access SSL private key.

However, in the proposed payment protocol, an application running on the server needs access to private key to be able to sign PaymentRequests. If this application is compromised, so is the key.

Secondly, this protocol can't be used securely with offline wallet because Payment structure is not signed so it can be modified by compromised customer's online computer. Modifications to refund_to attribute seem the most dangerous. Also, a merchant can reject the payment but still broadcast the transactions (possibly after some delay).

As far as I understand, thanke's proposal has none of these shortcomings.

Also, it doesn't depend on traditional PKI. Merchants may sign their master keys with SSL certificates, GPG certificates, or even both. So a normal customer can verify merchant's key using SSL certificate, but a paranoid customer, who doesn't trust governments and CAs but trusts GPG WOT, can verify the merchant's key using GPG.