For some organizations that use only a small subset of Windows Server 2003’s features and who have appropriately trained systems administrators, it may make sense to migrate some servers to Linux rather than to a newer version of Windows Server.
For example, rather than migrating a Windows Server 2003 DHCP server to Windows Server 2012 R2, some organizations may instead choose to implement a solution that has DHCP hosted on a computer running a Linux operating system.
While the idea of replacing a Microsoft server with one running a distribution of Linux might have seemed anathema a decade ago, it’s worth pointing out that many server management tools like Chef and Puppet can be used to manage servers running both Linux and Windows. Microsoft has also been working to bring tools like PowerShell to Linux and it might not be too long a bow to draw to hypothesize that one day it might be possible to use PowerShell Desired State Configuration to configure a server running Linux in the same way that it can be used to configure a computer running a Windows Server operating system.
The key to whether it is a good idea to replace services hosted on a Microsoft OS with services hosted on a Linux OS is whether or not your systems administration team is familiar with managing servers running Linux. If your team has skilled Linux systems administrators, then transitioning is definitely a reasonable option. If your team is unfamiliar with Linux, you are likely to be better off upgrading to Windows Server 2012 R2.