I don’t know if there is really a right answer to this question, and I don’t know what you find cumbersome about wp_localize_script, but you should be able to do it either way.
The difference is that with wp_localize_script the data is printed to the source of the page, which you wouldn’t want if the data were sensitive, and wp_localize_script should represent a wee bit less load on the server as it doesn’t require a separate connection as AJAX does.
I’d lean towards wp_localize_script unless there are compelling reasons to do something else.