You can specify that you want to copy an item only if the item is newer than the corresponding item at the destination. We call this process : Incremental Update. You need to use New-CopySettings command to specify that you want to copy incrementally. We use the source and destination modified date of the item to verify if the item is newer than the destination item or not. Note that if the item at the destination is deleted or moved under a different hierarchy, the incremental copy won't find any match and will create a new item. Also note that when using the insane mode on Office 365, all versions at the destination will be replaced by the versions from the source because of a limitation in the Azure Import API.
Here is an example when copying content between 2 lists :
$copysettings = New-CopySettings -OnContentItemExists IncrementalUpdate
$srcSite = Connect-Site -Url http://myfarm1/sites/mysourcesite
$dstSite = Connect-Site -Url http://myfarm1/sites/mydestinationsite
$srcList = Get-List -Name mysrclist -Site $srcSite
$dstList = Get-List -Name mydstlist -Site $dstSite
Copy-Content -SourceList $srcList -DestinationList $dstList -CopySettings $copysettings