Best way to do a hash compare of 2 folders

So I have two folders. The first folder has duplicate files that exist in the second folder. The problem is that in the second folder, the files are named very differently. Is there a way to do a hash compare of both folders, and then for it to tell me which files there is duplicates for in both folders, and which files there are not?

Here's a quick Powershell script:

Code:

function DoFolderHash([string]$folder1, [string]$folder2)
{
  $hashes1 = Get-ChildItem -Path "$folder1" -Recurse | Get-FileHash
  $hashes2 = Get-ChildItem -Path "$folder2" -Recurse | Get-FileHash
  $files = $hashes1.Path + $hashes2.Path
  ""
  "Identical files:"
  foreach($h1 in $hashes1)
  {
    foreach($h2 in $hashes2)
    {
      if($h1.Hash -eq $h2.Hash)
      {
        $h1.Path + " == " + $h2.Path
        $files = $files -ne $h1.Path
        $files = $files -ne $h2.Path
      }
    }
  }
  ""
  "Unique files:"
  $files
  ""
}

Copy+paste it into a Powershell window and run DoFolderHash <Folder 1> <Folder 2>

Code:

PS C:\Users\Me> DoFolderHash "c:\temp\1" "c:\temp\2"

Identical files:
C:\temp\1\HxD32.exe == C:\temp\2\a
C:\temp\1\HxD32.exe == C:\temp\2\e
C:\temp\1\HxD64.exe == C:\temp\2\g
C:\temp\1\readme.txt == C:\temp\2\f
C:\temp\1\Settings\HxD Hex Editor.ini == C:\temp\2\b
C:\temp\1\Settings\HxD Hex Editor.lang == C:\temp\2\c

Unique files:
C:\temp\1\changelog.txt
C:\temp\1\license.txt
C:\temp\2\d
C:\temp\2\h

PS C:\Users\Me>

Thanks all! I'll check both of these out.