This, of course, is not the final list of all the pros and cons, but rather the ones I came across when trying to implement Openfire's cross-network encrypted connection.
Socket One Pro Rim : supports automatic TLS encryption.
One possible way to connect sockets: I recently found out that using socket connections can be a problem if Openfire Server is on a different network than the client connecting to this server, in which case the ability to connect to the server may be under the control of the connecting network firewall and connectivity through the standard Socket 5222 port.
HTTP Bind
Pro for Http-Bind: May fix the aforementioned interconnect problem using the standard Http port.
One Http-Bind loop: does not support TLS automatic encryption and instead relies on the Old SSL standard for encrypted communications, which apparently is not supported by many XMPP libraries.
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