How to make two feature layers congruent using ArcGIS for Desktop?

I have two feature layers (polyline/polygon) which should be congruent but there's an offset of about 220 meters.

The Georeferencing tool only works with raster layers.

How do I do the equivalent with a feature layer?

Answer

In ArcMap use the Spatial Adjustment toolbar:

Within the editing environment, the spatial adjustment tools provide interactive methods to align and integrate your data. Spatial adjustment supports a variety of adjustment methods and will adjust all editable data sources. It's often used when you've imported data from another source, such as a CAD drawing.