Keep in mind I haven't tested this and it goes without says your working with copies of the parcel data specifically meant to be edited. I would try
1) Open the Attributes Fields for each parcel layer and turn off the visibility of all fields except the ObjectID, shape, and one other text field (probably something like RE).
2) Now that they have the bare minimum number of fields and the same schema (if they both contain the RE attributes and I'm assuming they do) export each to a new feature class by right clicking them in the Table of contents and selecting "Data" > "Export Features"
3) Merge these two together to get a third feature class containing all the parcels your interested in (using the Merge geoprocessing tool).
4) Open the attribute table of the resulting file and use Calculate Field to populate the "RE" attribute with the same value for every polygon.
5) Now that every polygon has the same value in RE you can use the "Dissolve" geoprocessing tool using RE to just get out outside edge of all the merged parcels.
Keep in mind that the format of the "RE" field (or whichever common field you chose) must match between the two merged files.
Also keep in mind your using thousand of polygons here so this could take a long time and depending on how well the two sources "edge match" where they should have a boundary in common (I.E. along the merge lines between the two sources) it could produce not "perfect" results.... you might have to clean it up a bit.