A key difference between XMPP and AMQP is binary content. AMQP handles binary data just fine, and XMPP seems more designed for XML. Personally for online games I use Google Protocol Buffers for message formatting and parsing, and with their very small binary footprint, I'd be more inclined to use AMQP to deliver those messages.
But do consider what AMQP server you want to use. I've been bitten by using RabbitMQ for my AMQP server in the past. RabbitMQ does not have any flow control facilities, at all. So if your clients are sending messages faster than your server can consume them, buffers on the server can fill up and blow the server up. More recent versions of RabbitMQ implement flow control in an exceedingly coarse way: they halt all consumers in the system until memory clears up.
I've never tried zeromq; perhaps it'd be better for the things I've been using RabbitMQ for...