partitioning by datetime vs date vs int performance
You shouldn't get any additional performance gain by adding the extra column. If any, I doubt it will outweigh the additional storage cost required for the extra column.

There is one perk that you'll get from having a date only column and that is that you can have a date dimension. If this is for a data warehouse, I'd definitely recommend including.

If you decide to add the additional column (and assuming you're on SQL 2008 +), use the Date datatype. Int (formatted in YYYYMMDD) used to be the recommended format for partitioning, as it was cheaper (@ 4 bytes/row) than datetime (@ 8 bytes/row). Date is 3 bytes/row and is in a natural date format. Also, INT is a pain in the butt to query on as you have to add conversions in your' search arguments:

WHERE DateID = (CONVERT([int],CONVERT([char](8),getdate(),(112)),(0)))