The following is the best method which maintains all the metadata for all the documents and items in the list.
1 Go to the source site. Save the site as a template (without including content).
2 Download the site template from the source site collection template gallery and upload it on the destination site template gallery.
3 Go to the destination site. Create a subsite within the destination site collaction with the uploaded site template.
This would ensure that we have the same site metadata information on the destination (but on a subsite).
4 Export the site from the source using stsadm. Make sure to include security and versioning while you export
(stsadm -o export -url
http://sourcesite/sourceweb -filename migrate.dat -includeusersecurity -versions 4)
5 Import the site to the newly created subsite on the destination through stsadm that has been exported.
(stsadm -o import –url
http://destinationsite/destinationweb/import -filename migrate.dat –nologfile -includeusersecurity -updateversions 2)
Now we have all the contents with its metadata on the destination site on one of its subsites.
6 Go to the subsite and create a template for the document library that you want to move (without including content).
7 Create a document library on the destination site with this template.
This ensures that all the columns of the document library are present in the destination.
8 Now go to the Manage content and structure on the destination site collection and move the document library from the subsite to the destination location.
Since you are on SP 2013 use PowerShell