It really depends what you're trying to do. For simplicity's sake, I would say that the first option (just load it with the appropriate query string variables in the URL) is better.
Rendering a page using AJAX is pretty much always more complicated. However, it also gives you much more control over the UI if you know what you're doing. From my experience, if you want your page to be more like a "web app" with dynamic things happening everywhere, it is much easier to simply load JSON data from the server via AJAX and to dynamically create views via some sort of templating system. Otherwise you're stuck with loading the DOM with PHP, and then somehow communicating that data to your JavaScript, either by using data-XXX attributes on DOM elements, having PHP output a JSON string at the top of a page and assign it to a JavaScript variable, etc. It could get very complicated and convoluted.
In your case it looks like you're just trying to allow users to view certain data from your forum. Barring any additional requirements, I would recommend going with the first option because it will be much easier. This is simple enough that you don't seem to need to load anything dynamically.
A good rule of thumb is the more complicated and dynamic your UI, the more you should think about moving to a "web app" framework, and just let the server act as a REST server.
