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We upgraded Sitecore 8.2 project to 9.1. Upgrade took around 1 month to finish and during this period, authors created/updated some items in old instance and they didn't make a note of those items.

So, now I want to compare both instances to find out items to migrate content from 8.2 to 9.1

Is there any way to find out what items got updated/created in old instance? Can this be done using Sitecore Powershell Remoting?

There are a few options included with SPE out-of-the-box which could aid in accomplishing this task. The detail below is produced with SPE 6.0 but much of it was available in previous versions.

Reports

There is a Content Report called Items last updated which can be used to find any items in the tree (typically content) that has changed after a specified date.

Comparing Instances

The following script provides a basic example at using SPE to compare the content between two instances beginning with the specified root item.

Clear-Host
$watch = [System.Diagnostics.Stopwatch]::StartNew()

$Username = "admin"
$Password = "b"
$Source = "https://abc.dev.local"
$Destination = "https://123.dev.local"

$localSession = New-ScriptSession -user $Username -pass $Password -conn $Source
$remoteSession = New-ScriptSession -user $Username -pass $Password -conn $Destination


$rootId = "37D08F47-7113-4AD6-A5EB-0C0B04EF6D05"

$sourceItemIds = Invoke-RemoteScript -Session $localSession -ScriptBlock 
 $rootItem = Get-Item -Path "master:" -ID $using:rootId

 $itemIds = (@($rootItem) + @($rootItem.Axes.GetDescendants()) -Raw

$destinationItemIds = Invoke-RemoteScript -Session $remoteSession -ScriptBlock Select-Object -ExpandProperty ID) -join " -Raw

$referenceIds = $sourceItemIds.Split("|", [System.StringSplitOptions]::RemoveEmptyEntries)
$differenceIds = $destinationItemIds.Split("|", [System.StringSplitOptions]::RemoveEmptyEntries)

$queueIds = Compare-Object -ReferenceObject $referenceIds -DifferenceObject $differenceIds | 
 Where-Object $_.SideIndicator -eq "<=" | Select-Object -ExpandProperty InputObject

$watch.Stop()
$totalSeconds = $watch.ElapsedMilliseconds / 1000
Write-Host "$($totalSeconds) seconds" -ForegroundColor Yellow

Welcome to Sitecore stackexchange.

RAZL RAZL - can be used to compare the items between two different Sitecore Instances. Please note this is a "paid" software.

Another option is to use Sitecore Courier - This open source module can compare sitecore serialized files in two folders and create a diff (update) package containing the differences.

There is also more information on this other post which you can refer - Comparing a Sitecore instance with a vanilla one