Looks like you are using wp super cache. My initial guess would be that your main page is a lot more likely to be cached that any of the deeper pages since it gets hit more frequently. A caching plugin can help hide really slow back-end issues but it doesn’t really “fix” the issue.
Can you enable debugging of some kind for wp-super-cache to see if it is able to cache the deeper pages or if not, why?
Dear Patrick, thank you very much for you reply. Actually I’m using only wp super cache and wp widget cache. I already deactivated the last one, but with no effect. I`m still wondering that all subpages perform constantly bad - especially regarding compress transfer and images - while the home is far more “green”. I’d be happy if you could help me with the wp super cache debugging protocol: