I think its best to streak the inhibitor strain first and the sensitive strains second. That way it is much easier to observe the degree of inhibition because you will get little or no growth for the entire length after the intersection. However if you do the reverse then you will only observe inhibition at the point of intersection.  

Thank you for the answer @Michael J. Benedik, please would you be able to explain the rationale behind this. I have been trying to reason it out but not getting it. I am comparing the cross streak method with agar well or disk diffusion in which case the sensitive strain goes in first

The reason is that when you streak the sensitive strain across the inhibitor producing strain, then you are carrying inhibitor cells along. So the sensitive strain will mostly die the entire length of the streak after it crosses the inhibitor strain. 

One important thing is whether you are trying to be quantitative or just screening lots of samples. If you are screening for possible inhibitor strains against a single sensitive strain, then you want to use some method that makes it easy, such as spots on a sensitive lawn. If you are screening multiple sensitive strains against a single inhibitor strain, then cross streaking works well. But if you want to be more quantitative then some type of disk assay where you can measure the zone of inhibition might be best. 

It makes whole lots of sense to me now. I am grateful

Obviously the horizontal streak.

What are the type of microbes you are testing? Bacteria, actinobacteria or fungi? T.he testing methods are different for each