Your comment piqued my curiosity, so I added up the SOS for the two teams. The first thing I noticed was that Washington's SOS was 111-114; yet on Tankathon it shows their SOS is over .500. Apparently they calculate teams' SOS based on their entire schedule and not just on the games they have already played.
When I added in both of those two final games, the results are incredibly similar. Washington went from 111-114 to 132-123 with the addition of those last two games, while the Patriots moved from 118-107 SOS to 133-122 - a mere one game difference.
Should Washington and New England finish with the same record, the SOS could easily go to either team. However, if the Pats win once and certain other teams lose twice, they could concevably fall to as low as the #7 pick! The reason for that is that draft order tiebreakers are different from playoff tiebreakers. The head to head victories/losses matter for the playoffs, but SOS is the number one (and usually only) determining factor for thee draft - which means the Giants, Chargers and possibly Tennessee could all leapfrog the Patriots in the draft order if the Pats defeat the Jets.