First of all, Network engineer are related to hardware infrastructure like Routers and Switches and that lead to Cisco or any related network infrastructure providers. On the other hand, System engineers are related to software, to be more specific Network Operating System and that lead to Microsoft or any related network operating system providers.
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Muhammad Shoaib Ayaz , Senior Network Engineer , Immigration Passport Headquarters MRP Project
If you got at least professional level certification of Cisco or any famous Networking vendor with at least1 year hands on experience than go for Network side, but if you that much qualification in Network than simply move to system side.
System side you may find plenty of jobs in the market, cause almost every cooperate sector requirement is System Administrator. So if you have good LAN, WAN knowledge with system Expertise, I guess you'll be having more opportunities in the market.
Networking is the best way but having multiple skills is more preferable for job seekers.
Plan to learn Networking, Telephony(voice), virtualization, Cloud i feel these technologies will never have end point
The concept of having dedicated Network Engineer or System Administrator is vanishing slowly with cloud service market grows bigger day by day .most of technology leaders vendor looking to new generation of administrator refer to them by (" infrastructure administrator") like (“CCNA Data Center certification”) which can manage virtual setup and networking in some cases storage also due technology trend and moving everything to virtual environment .