First, you should make sure not to mix up »hits«, »files«, »visits« and »unique visits«. They all have a different meaning and are sometimes called differently. I recommend you to look up some definitions if you are confused about the terms.
awstats has probably the most correct statistics, because it has access to the access.log from the web server. Unfortunately, a cached site (maybe cached by the browser, a proxy from an ISP or your own caching server) might not produce a hit on the web server. Especially if your site is served with good caching hints which don't enforce a revalidation and you are running your own web cache (e.g. Squid) in front of your site, the number will be considerable lower, because it only measures the work of the web server.
On the other hand, Google Analytics is only able to count requests from users which haven't blocked Google Analytics and have JavaScript enabled (but they will count pages served by a web cache). So, this count can be influenced by the user, but isn't affected by web caches.
The ad-company is probably simply counting the number of requests which they get from your site (probably based on their access.log). So, to get counted there, the add must not be cached and must not be blocked by the user.
So, as you can see, it's not that easy to get a single correct value. But as long as you use the measured values in comparison to those from the previous months, you should get at least a (nearly) correct rate of growth.
And your porn site probably serves a high amount of static content (e.g. images from the disk) and most of the web servers are really good at serving caching hints automatically for static files. Your MMORPG on the other hand, might mostly consist of some dynamic scripts (PHP?) which don't send any caching hints at all and web servers aren't able to determine those caching headers for dynamic content automatically. That's at least my explanation, without knowing your application and server configuration :)