Is there a XDomainRequest equivalent in Firefox?

The XDomainRequest object in Internet Explorer 8 is a proprietary method for requesting resources which are outside the "same-origin policy."

Firefox 3.5+ and Safari 4+ allow cross-domain requests through the XMLHTTPRequest object. User agents that support XMLHTTPRequest Level 2 must have Cross-Origin Resource Sharing support (CORS), which allows retrieving the resource IF the resource announces that it can be requested from other domains.

Keep in mind that the resource must declare itself as a cross-origin resource before a compliant user agent will retrieve the resource.

More info here: http://www.w3.org/TR/cors/ and at /TR/XMLHttpRequest2 on the W3C website.

It's possible, you just have to set Cross-Domain headers at the target server.

.htaccess example:

Header set Access-Control-Allow-Origin "*"
Header set Access-Control-Allow-Headers "X-Requested-With"
Header set Access-Control-Max-Age "60"

XmlHttpRequest will submit an OPTIONS request to the target server which will respond with those headers, allowing the client to submit the intended request.

Source: http://www.oriontransfer.co.nz/blog/2011-05/cross-domain-ajax/index