This is more a religious issue than a technical one. Esri supports both Linux and Windows platforms, without regard to which one is "better".
There are a few technical issues which could steer you to one platform or the other (e.g., Direct Connect to MS SQL Server enterprise geodatabase is not possible from Linux, or the only version of Windows supported by your IT department is under the minimum or over the maximum required for ArcGIS), but from my experience, Server is startlingly OS agnostic.
Utilizing a new OS may have a ramp-up cost (if it's new to your IT infrastructure), but once the install is complete, the Server software behaves the same from a client standpoint. The usual hitches in porting between platforms are tied to customized extensions and the curious way case dependency is handled when migrating from case-neutral path strings of Windows to case-dependent paths in Linux.
- V