What are the advantages/disadvantages of using jQuery DOM manipulation as opposed to PHP DOM manipulation?

PHP is running on the server, JavaScript in the client.

This means PHP is faster (more resources), the result can be cached, and you have to test only one interpreter.

JavaScript – you don’t really need jQuery for this – is more error prone, because of weird clients, blocked resources, or a more limited available memory. However it can respond to user input immediately without an extra page load.

If you have a situation in which both ways are leading to the same result, go for the server side.