Does using Drupal.ajax() offer any benefits over jQuery.ajax()? I'm updating a node's references (list of them - rendered entities) manually with AJAX and experiencing performance problems.

$.ajax() is used to call a view rendered with the simplest page.tpl.php ever: print render($page['content']).

The filters are simple exposed filters that I pre-handle in the URL level so the url looks like this: /url-of-view?argone=foo&amp;argtwo=bar&amp;template=minimal. The view is then built up, rendered, and returned to the client.

The problem is when the site is at it's peak hours this URL (normally) is being bombarded and the server becomes slow to borderline unresponsive.

Will using Drupal.ajax() instead of jQuery.ajax() give me a performance boost here, or should I look at querying the node data manually instead of relying on Views?
There isn't really any difference in this context; at the lowest level both will use a standard XHR, so I reckon there's a good chance the bottleneck is the server-side building of the View. 

You can test that by profiling, or in a pinch, returning a static string from the AJAX callback temporarily and stress testing the server. If you don't see the bottleneck, you know that building the View is the expensive bit.

If you're able to build up a query for the node data, and render the HTML manually, you should definitely see a performance improvement. A that point, though, you might want to question if using Views is the right thing in the first place :)