I would like to know, if there exists any solution in order to synchronize (replicate) sessions between two httpd servers which are configured as load balancers using mod_proxy_balancer?
Store the session information in a cookie as explained in the mod_proxy_balancer documentation. In that way the client will provide the session info to apache, no matter which one it lands on (assuming both of them are configured identically). This implies usage of sticky sessions. As far as I'm aware this is the way HAProxy does it as well. Can you please elaborate on which HAProxy (different) functionality you are talking about in regards of sticky table synchronization?