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.
Source: http://dzeee.net/sharepoint/post/2010/01/17/Copy-content-from-one-site-collection-to-another-preserving-metadata.aspx
Since you are on SP 2013 use PowerShell Export-SPWeb
and Import-SPWeb
http://technet.microsoft.com/en-us/library/ff607895(v=office.15).aspx
http://sharepoint-community.net/profiles/blogs/how-to-export-import-a-list-using-powershell