I don't know if there is an easy way to do this directly in C# but you could do an unmanaged call to GetFileInformationByHandle (pinvoke page here) which will return a BY_HANDLE_FILE_INFORMATION structure. This contains three fields which can be combined to uniquely ID a file:
dwVolumeSerialNumber:
The serial number of the volume that contains a file.
...
nFileIndexHigh:
The high-order part of a unique identifier that is associated with a
file.
nFileIndexLo:
The low-order part of a unique identifier that is associated with a
file.
The identifier (low and high parts) and the volume serial number uniquely identify a file on a single computer. To determine whether two open handles represent the same file, combine the identifier and the volume serial number for each file and compare them.
Note though that this only works if both references are declared from the same machine.
Edited to add:
As per this question this may not work for the situation you have since the dwVolumeSerialNumber may be different is the share definitions are different. I'd try it out first though, since I always thought that the volume serial number was drive specific, not path specific. I've never needed to actually prove this though, so I could be (and probably am) wrong.