I want to format and reboot my old 15" MacBook Pro year 2009 (2.4 GHz, Intel Core 2 Duo, RAM 8 GB). I'll use it with Office, Chrome and VLC, nothing else. Given that, what's the best choice between Mountain Lion and Maverick?
First of all assuming that your hardware is per requirement for either OS.
The 3 apps you mentioned, you will not notice speed improvement in VLC or Office 2011 since those apps are not really speed dependent, but since Mavericks has better overall process task management it could be faster.
If you were to use Safari instead of Chrome you would notice improved speed in Safari with Mavericks.
The Mavericks does have a better memory (RAM) management them ML that can be helpful even for Office and VLC to make them work faster.
If you care about batter utilization then mavericks wins that one.
In summary, generally new software are always better (faster) the older one, otherwise they would defeat the purpose of been released as a improvement.