OK, I'm not going to code the whole thing for you (what's the fun in that?) but I'll get you started.

First, there are two ways to do the content comparison. The lazy/mostly right way, which is comparing the length of the files; and the accurate but more involved way, which is comparing a hash of the contents of each file.

For simplicity sake, let's do the easy way and compare file size.

Basically, you want two objects that represent the source and target folders:

$Folder1 = Get-childitem "C:\Folder1"$Folder2 = Get-childitem  "C:\Folder2"

Then you can use Compare-Object to see which items are different...

Compare-Object $Folder1 $Folder2 -Property Name, Length

which will list for you everything that is different by comparing only name and length of the file objects in each collection.

You can pipe that to a Where-Object filter to pick stuff that is different on the left side...

Compare-Object $Folder1 $Folder2 -Property Name, Length | Where-Object {$_.SideIndicator -eq "<="}

And then pipe that to a ForEach-Object to copy where you want:

Compare-Object $Folder1 $Folder2 -Property Name, Length  | Where-Object {$_.SideIndicator -eq "<="} | ForEach-Object {        Copy-Item "C:\Folder1\$($_.name)" -Destination "C:\Folder3" -Force        }

Recursive Directory Diff Using MD5 Hashing (Compares Content)

Here is a pure PowerShell v3+ recursive file diff (no dependencies) that calculates MD5 hash for each directories file contents (left/right). Can optionally export CSV's along with a summary text file. Default outputs results to stdout. Can either drop the rdiff.ps1 file into your path or copy the contents into your script.

USAGE: rdiff path/to/left,path/to/right [-s path/to/summary/dir]

Here is the gist. Recommended to use version from gist as it may have additional features over time. Feel free to send pull requests.

############################################################################ USAGE: rdiff path/to/left,path/to/right [-s path/to/summary/dir]  ###### ADD LOCATION OF THIS SCRIPT TO PATH                               ############################################################################[CmdletBinding()]param (  [parameter(HelpMessage="Stores the execution working directory.")]  [string]$ExecutionDirectory=$PWD,  [parameter(Position=0,HelpMessage="Compare two directories recursively for differences.")]  [alias("c")]  [string[]]$Compare,  [parameter(HelpMessage="Export a summary to path.")]  [alias("s")]  [string]$ExportSummary)### FUNCTION DEFINITIONS #### SETS WORKING DIRECTORY FOR .NET #function SetWorkDir($PathName, $TestPath) {  $AbsPath = NormalizePath $PathName $TestPath  Set-Location $AbsPath  [System.IO.Directory]::SetCurrentDirectory($AbsPath)}# RESTORES THE EXECUTION WORKING DIRECTORY AND EXITS #function SafeExit() {  SetWorkDir /path/to/execution/directory $ExecutionDirectory  Exit}function Print {  [CmdletBinding()]  param (    [parameter(Mandatory=$TRUE,Position=0,HelpMessage="Message to print.")]    [string]$Message,    [parameter(HelpMessage="Specifies a success.")]    [alias("s")]    [switch]$SuccessFlag,    [parameter(HelpMessage="Specifies a warning.")]    [alias("w")]    [switch]$WarningFlag,    [parameter(HelpMessage="Specifies an error.")]    [alias("e")]    [switch]$ErrorFlag,    [parameter(HelpMessage="Specifies a fatal error.")]    [alias("f")]    [switch]$FatalFlag,    [parameter(HelpMessage="Specifies a info message.")]    [alias("i")]    [switch]$InfoFlag = !$SuccessFlag -and !$WarningFlag -and !$ErrorFlag -and !$FatalFlag,    [parameter(HelpMessage="Specifies blank lines to print before.")]    [alias("b")]    [int]$LinesBefore=0,    [parameter(HelpMessage="Specifies blank lines to print after.")]    [alias("a")]    [int]$LinesAfter=0,    [parameter(HelpMessage="Specifies if program should exit.")]    [alias("x")]    [switch]$ExitAfter  )  PROCESS {    if($LinesBefore -ne 0) {      foreach($i in 0..$LinesBefore) { Write-Host "" }    }    if($InfoFlag) { Write-Host "$Message" }    if($SuccessFlag) { Write-Host "$Message" -ForegroundColor "Green" }    if($WarningFlag) { Write-Host "$Message" -ForegroundColor "Orange" }    if($ErrorFlag) { Write-Host "$Message" -ForegroundColor "Red" }    if($FatalFlag) { Write-Host "$Message" -ForegroundColor "Red" -BackgroundColor "Black" }    if($LinesAfter -ne 0) {      foreach($i in 0..$LinesAfter) { Write-Host "" }    }    if($ExitAfter) { SafeExit }  }}# VALIDATES STRING MIGHT BE A PATH #function ValidatePath($PathName, $TestPath) {  If([string]::IsNullOrWhiteSpace($TestPath)) {    Print -x -f "$PathName is not a path"  }}# NORMALIZES RELATIVE OR ABSOLUTE PATH TO ABSOLUTE PATH #function NormalizePath($PathName, $TestPath) {  ValidatePath "$PathName" "$TestPath"  $TestPath = [System.IO.Path]::Combine((pwd).Path, $TestPath)  $NormalizedPath = [System.IO.Path]::GetFullPath($TestPath)  return $NormalizedPath}# VALIDATES STRING MIGHT BE A PATH AND RETURNS ABSOLUTE PATH #function ResolvePath($PathName, $TestPath) {  ValidatePath "$PathName" "$TestPath"  $ResolvedPath = NormalizePath $PathName $TestPath  return $ResolvedPath}# VALIDATES STRING RESOLVES TO A PATH AND RETURNS ABSOLUTE PATH #function RequirePath($PathName, $TestPath, $PathType) {  ValidatePath $PathName $TestPath  If(!(Test-Path $TestPath -PathType $PathType)) {    Print -x -f "$PathName ($TestPath) does not exist as a $PathType"  }  $ResolvedPath = Resolve-Path $TestPath  return $ResolvedPath}# Like mkdir -p -> creates a directory recursively if it doesn't exist #function MakeDirP {  [CmdletBinding()]  param (    [parameter(Mandatory=$TRUE,Position=0,HelpMessage="Path create.")]    [string]$Path  )  PROCESS {    New-Item -path $Path -itemtype Directory -force | Out-Null  }}# GETS ALL FILES IN A PATH RECURSIVELY #function GetFiles {  [CmdletBinding()]  param (    [parameter(Mandatory=$TRUE,Position=0,HelpMessage="Path to get files for.")]    [string]$Path  )  PROCESS {    ls $Path -r | where { !$_.PSIsContainer }  }}# GETS ALL FILES WITH CALCULATED HASH PROPERTY RELATIVE TO A ROOT DIRECTORY RECURSIVELY ## RETURNS LIST OF @{RelativePath, Hash, FullName}function GetFilesWithHash {  [CmdletBinding()]  param (    [parameter(Mandatory=$TRUE,Position=0,HelpMessage="Path to get directories for.")]    [string]$Path,    [parameter(HelpMessage="The hash algorithm to use.")]    [string]$Algorithm="MD5"  )  PROCESS {    $OriginalPath = $PWD    SetWorkDir path/to/diff $Path    GetFiles $Path | select @{N="RelativePath";E={$_.FullName | Resolve-Path -Relative}},                            @{N="Hash";E={(Get-FileHash $_.FullName -Algorithm $Algorithm | select Hash).Hash}},                            FullName    SetWorkDir path/to/original $OriginalPath  }}# COMPARE TWO DIRECTORIES RECURSIVELY ## RETURNS LIST OF @{RelativePath, Hash, FullName}function DiffDirectories {  [CmdletBinding()]  param (    [parameter(Mandatory=$TRUE,Position=0,HelpMessage="Directory to compare left.")]    [alias("l")]    [string]$LeftPath,    [parameter(Mandatory=$TRUE,Position=1,HelpMessage="Directory to compare right.")]    [alias("r")]    [string]$RightPath  )  PROCESS {    $LeftHash = GetFilesWithHash $LeftPath    $RightHash = GetFilesWithHash $RightPath    diff -ReferenceObject $LeftHash -DifferenceObject $RightHash -Property RelativePath,Hash  }}### END FUNCTION DEFINITIONS ###### PROGRAM LOGIC ###if($Compare.length -ne 2) {  Print -x "Compare requires passing exactly 2 path parameters separated by comma, you passed $($Compare.length)." -f}Print "Comparing $($Compare[0]) to $($Compare[1])..." -a 1$LeftPath   = RequirePath path/to/left $Compare[0] container$RightPath  = RequirePath path/to/right $Compare[1] container$Diff       = DiffDirectories $LeftPath $RightPath$LeftDiff   = $Diff | where {$_.SideIndicator -eq "<="} | select RelativePath,Hash$RightDiff   = $Diff | where {$_.SideIndicator -eq "=>"} | select RelativePath,Hashif($ExportSummary) {  $ExportSummary = ResolvePath path/to/summary/dir $ExportSummary  MakeDirP $ExportSummary  $SummaryPath = Join-Path $ExportSummary summary.txt  $LeftCsvPath = Join-Path $ExportSummary left.csv  $RightCsvPath = Join-Path $ExportSummary right.csv  $LeftMeasure = $LeftDiff | measure  $RightMeasure = $RightDiff | measure  "== DIFF SUMMARY ==" > $SummaryPath  "" >> $SummaryPath  "-- DIRECTORIES --" >> $SummaryPath  "`tLEFT -> $LeftPath" >> $SummaryPath  "`tRIGHT -> $RightPath" >> $SummaryPath  "" >> $SummaryPath  "-- DIFF COUNT --" >> $SummaryPath  "`tLEFT -> $($LeftMeasure.Count)" >> $SummaryPath  "`tRIGHT -> $($RightMeasure.Count)" >> $SummaryPath  "" >> $SummaryPath  $Diff | Format-Table >> $SummaryPath  $LeftDiff | Export-Csv $LeftCsvPath -f  $RightDiff | Export-Csv $RightCsvPath -f}$DiffSafeExit

Further to @JNK's answer, you might want to ensure that you are always working with files rather than the less-intuitive output from Compare-Object. You just need to use the -PassThru switch...

$Folder1 = Get-ChildItem "C:\Folder1"$Folder2 = Get-ChildItem "C:\Folder2"$Folder2 = "C:\Folder3\"# Get all differences, i.e. from both "sides"$AllDiffs = Compare-Object $Folder1 $Folder2 -Property Name,Length -PassThru# Filter for new/updated files from $Folder2$Changes = $AllDiffs | Where-Object {$_.Directory.Fullname -eq $Folder2}# Copy to $Folder3$Changes | Copy-Item -Destination $Folder3

This at least means you don't have to worry about which way the SideIndicator arrow points!

Also, bear in mind that you might want to compare on LastWriteTime as well.

Sub-folders

Looping through the sub-folders recursively is a little more complicated as you probably will need to strip off the respective root folder paths from the FullName field before comparing lists.

You could do this by adding a new ScriptProperty to your Folder1 and Folder2 lists:

$Folder1 | Add-Member -MemberType ScriptProperty -Name "RelativePath" `  -Value {$this.FullName -replace [Regex]::Escape("C:\Folder1"),""}$Folder2 | Add-Member -MemberType ScriptProperty -Name "RelativePath" `  -Value {$this.FullName -replace [Regex]::Escape("C:\Folder2"),""}

You should then be able to use RelativePath as a property when comparing the two objects and also use that to join on to "C:\Folder3" when copying to keep the folder structure in place.