This can be done in PowerShell using the shell.application com object.
Assuming:
C:\Test
│ Zipped1.zip (conains new1.txt, new2.txt, new3.txt)
│ Zipped2.zip (conains new4.txt, new5.txt, new6.txt)
│
└───UnZipped
New1.txt
New2.txt
New3.txt
New4.txt
new5.txt
new6.txt
$UnzippedFilePath = 'C:\tEST\UnZipped'
$ZippedFilePaths = @'
C:\tEST\Zipped1.zip
C:\tEST\Zipped2.zip
'@ -split "`n"
### Note: If Explorer optioins are set to hide known extensions,
### "$_.Name" will have no extension.
### Splitting "$_.Path" ensures the extension is inclueded
$ZippedFileNames = $ZippedFilePaths.ForEach{@($shell.NameSpace($_).Items()).ForEach{$_.Path.Split('\')[-1]}}
$UnzippedFileNames = (Get-ChildItem $UnzippedFilePath).Name
### This returns names that don't match
Compare-Object $ZippedFileNames $UnzippedFileNames
### This returens names that are matched
Compare-Object $ZippedFileNames $UnzippedFileNames -IncludeEqual
Output (from -IncludeEqual)
InputObject SideIndicator
----------- -------------
New1.txt ==
New2.txt ==
New3.txt ==
New4.txt ==
new5.txt ==
new6.txt ==