"even the server hardware is better than the older version moodle's server!"
Suggests there is more being changed than just the Moodle version.
If your hardware has changed have you checked compatibility with your linux software - and just as an aside Ubuntu server 16.04 is the latest LTS Ubuntu release, so you could try updating your OS software at the same time as your server hardware.
Have you updated your php/apache and all the background software, including migrating the database type (antelope-barracuda as per the upgrade warnings), have all your php settings been adjusted on the new server?
What testing have you done to make sure that, of all your changes, you have identified Moodle as the bottleneck (it may be, but given the changes involved in a new server it would be helpful to know what else you have tested and eliminated, as Moodle may not be the cause of the slow down )?