Hi Mihai,
Yes or no - it depends
There are times when having a central logging system is very valuable (sometimes even mandatory). In other cases it just complicates matters and increases network traffic for no good reason. Part of being a developer is to recognize that such issues exist and hopefully come up with a proposal.
In this particular case I
personally would
probably go with seperate log files - one for the server, and one for each client.
Regards, Andrew