ajax polling with admin-ajax.php

You idea is equivalent to DDOSing your site, and the difference between the methods is only how fast you will bring the site down.

WordPress AJAX handling is expensive, and should be limited to user initiated actions. Your second method will be more resilient but you are still going to be wasting server resources as initializing PHP by itself has cost, and usually the server is configured on handle on a limited amount of requests in a time, and your “polling” will leave less available “connection slots” for actual page views.