Server certificates (those that you'd use to enable HTTPS on a web server) are rarely enabled for code signing. I haven't looked at every CA in the world, and there probably are exceptions, but the more "legit" a CA is, the less likely they are to issue one certificate for both applications. In the end, I wouldn't expect to use the same certificate for both.
There is a better chance that a single code-signing certificate is accepted by most platforms. The developer documentation of each platform should list what CA certificates are built-in as trusted roots. In addition, most platforms will allow a user to view and modify the list.