I have multiple polygons that show me metropolitan areas and rural areas across a state. I want to modify the layer so that there are no rural polygons by assigning portions of the rural polygons to the metro polygons. This would ideally be a distance based operation, i.e., the areas of a rural polygon would be dissolved into the metro polygon that they are nearest to.
This is an ideal raster situation and can be resolved with a simple tool function.
For ESRI software the tool is called Nibble: http://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-analyst-toolbox/nibble.htm
You'll need to assign your areas a unique numerical ID, convert only your metro areas (rural = NoData) as a layer to use as a mask, and convert your entire dataset to raster as the input. Then you can convert your raster back to polygon based on the unique ID and join any other attributes you wish from your initial dataset.