Simply as you won't have to Create a new Object for using Path.GetFilename() it will perform better.
Here is a Comparison for both:
Code:
Path.GetFileName("G:\u.png")
IL:
IL_0000: ldstr "G:u.png"
IL_0005: call System.IO.Path.GetFileName
Code:
new FileInfo("G:\u.png").Name
IL:
IL_0000: ldstr "G:u.png"
IL_0005: newobj System.IO.FileInfo..ctor
IL_000A: callvirt System.IO.FileSystemInfo.get_Name
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