Salman do you have an Advanced license could you run feature to point on your small polygons and select the optional inside radio button. You should have points inside the polygons with the associated data you could then rerun the spatial join using the match option intersects and don't forget to set up your join field.
I'm sorry join is a property of the Spatial Join tool
Thank you. That was very helpful. I did it but one little problem with one row. You can see in the picture. There are clearly two polygons (Monschau and Simmerath) joined inside the selected polygon. But the table just lists Monschau alone. I don't understand why. In dissolve I selected CONTAINS as the join type.
Yes I did exactly what I did before except changing the match option to have their center in. I think the above results are correct for that match option. Only the little polygons inside which the larger polygons' centers lie are listed.
Salman are you willing to post another screen shot with the little polygons on the bottom with a grey outline and the big polygons on top with no fill and a thick red outline?