var path1 = Path.GetFullPath(@"c:\Some Dir\SOME FILE.XXX");
var path2 = Path.GetFullPath(@"C:\\\SOME DIR\subdir\..\some file.xxx");
// outputs true
Console.WriteLine("{0} == {1} ? {2}", path1, path2, string.Equals(path1, path2, StringComparison.OrdinalIgnoreCase));
Ignoring case is only a good idea on Windows. You can use FileInfo.FullName in a similar fashion, but Path will work with both files and directories.
Not sure about your second example.