Hello ,
If you have the choice between management with ASDM and through FPMC (which can also run virtually on ESXi), choose FPMC as that is much more powerful then the management through ASDM. When you manage via ASDM , you can see only real time connection events . Using an FMC you can get the full view of connection events and based on the database settings you can decide how much events you want to store.
http://www.cisco.com/c/en/us/products/security/firesight-management-center/index.html
Licensing Information as follows:-
http://www.cisco.com/c/en/us/td/docs/security/firepower/60/configuration/guide/fpmc-config-guide-v60/Licensing_the_Firepower_System.html
http://www.cisco.com/c/en/us/td/docs/security/firepower/roadmap/firepower-licenseroadmap.html
Rate if the post helps you.
Regards
Jetsy