You need to first transform data1, in your case by calling ToString()
on each element.
List<int> data1 = new List<int> {1,2,3,4,5};
List<string> data2 = new List<string>{"6","3"};
var newData = data1.Select(i => i.ToString()).Intersect(data2);
List<int> data1 = new List<int> {1,2,3,4,5};
List<string> data2 = new List<string>{"6","3"};
var newData = data1.Intersect(data2.Select(s => int.Parse(s));
Note that this will throw an exception if not all strings are numbers. So you could do the following first to check:
int temp;
if(data2.All(s => int.TryParse(s, out temp)))
{
// All data2 strings are int's
}