If you have the Advanced licence, you can use the Feature to Point tool to create points at the centroid of the 200m x 40m polygon and then use the Spatial Join tool to add the data from the points to the 200m x 60m polygon.
The process is a bit longer if you have the Basic or Standard licence. Add two fields, one with the Name 'X' and type 'Float' and the other Name 'Y' and Type 'Float' to the 200m x 40m polygon. Open the attribute table and right click on the new X field and click Calculate Geometry. Under the property drop down menu select 'X Coordinate of Centroid'. Do the same for the Y field, but choose 'Y Coordinate of Centroid'
With the attribute table still open click on the Table Options in the top left and select 'Export...' Export the table and make sure you add it to the current map. The table will appear in the TOC. Right click on it, and select 'Display X Y Data...'. The centroid points will appear as whatever you named the table + 'Events'. Right click on the new points and click 'Data' then 'Export Data...' and name it whatever you want. You will have the centroids of the polygons to then use with the Spatial Join tool.
However, this solution does not deal with the issue that radouxju has raised in the comments, notably what to do when two centroid points are within one polygon. You will end up losing data from one of the polygons.