Are you sure about that? You are now evaluating a string on one side to a date on the other. Do you know what really happens there? It will promote your string to a datetime. In other words you are explicitly casting a datetime to a string and then the sql engine will implicitly convert it right back to a datetime. This is good because if the engine compared them as strings your logic would not work correctly.

Take a look at the values from your convert.

SELECT RangeType,StartDate,EndDate,Comment

,convert(char(10),EndDate,102) as ConvertEndDate, cast('01 Oct 2013' as datetime)

, convert(char(10),StartDate,102) as ConvertStartDate, cast('01 Nov 2013' as datetime)

FROM dbo.TestTable

WHERE convert(char(10),EndDate,102) >= cast('01 Oct 2013' as datetime)

AND convert(char(10),StartDate,102) <= cast('01 Nov 2013' as datetime)

And adding the functions around EndDate and StartDate in your where clause has rendered this query nonsargable to boot.