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Both the roles are Important.
System Administrator maintains the customized/non-customized build of the Operating System and other roles which the employees require to be productive, and Network Administrator are responsible not only for networking but also for Telephony. Both are interdependent on each other, without Network, System Administration is not useful and vice versa.
In fact, both the jobs shall be given to them who knows about each others jobs. Like, the system administrator shall know the job roles or network admin and network admin shall know what all is covered by system administrator, so that they can both work together to avoid confusion and make good use the available resources.
The person who has System Administration Skills as well as Network Administration Skills is mostly chosen by Organizations for such jobs.