Boost VS Drupal Cache
Boost bypasses execution of Drupal's PHP and serves static files.  So unless you have other problems, it should always be much faster than the standard Drupal cache.  Be aware that it only works for anonymous users.

View source on your pages when running boost and make sure they have a comment at the end that says cached by boost.  Boost puts that comment there by default.  If you haven't disabled it, and it's not there, boost isn't working properly.  It's usually caused by incorrect or missing .htaccess rules.  If you don't see this comment, you won't see an error on the status page.  Your site will work normally, but is not being cached.

It looks like this:

&lt;/body&gt;
&lt;/html&gt;
&lt;!-- Page cached by Boost @ 2012-10-30 15:01:23, expires @ 2012-10-31 15:01:23 --&gt;