SQLNCLI10.x vs 11.x when connecting SSIS 2008R2 to a SQL Server 2012 database
According to this and this, there are upgrades to the sqlcmd.exe utility that I am assuming are reflective of underlying changes in the libraries. For instance, 


  Beginning in the ODBC Driver 11 for SQL Server, there is no limit on the amount of data that retrieved in a single column when –y0 is specified. 


I realize that this says the ODBC driver, but according to another link (that I can't post because of reputation limits), the SQLNCLI is some kind of wrapper for the ODBC drivers.


  The SQL Server Native Client...contains the SQL Server ODBC driver for Linux and  ODBC/ OLE DB provider for Windows ,  supporting native connectivity to Microsoft SQL Server.


From my limited searching, there don't appear to be any issues with using 10 to connect to a later sql server instance, but if there are SQL server features from that instance that you're taking advantage of, and you need access to them from your packages, then you're going to want to upgrade.

I can't speculate on performance, and would recommend benchmarking the two methods on your dev box to see what the differences are.

You are certainly losing functionality. I can't find any release notes that would indicate what functionality, per se, but the links above seem to hint at their being sql server specific functionality that is included in the NCLI APIs.