This season, they also share a similar downfall: too much of the time, they're not good enough.
Dallas (5-6) and Washington (5-6) are tied for second place in the NFC East, far in back of division-leading Philadelphia. The Cowboys and Redskins are also lagging behind in the race for a wild-card playoff berth.
"Inconsistency from the whole team probably is where we stand," Redskins coach Jay Gruden said on Monday. "Offensively, defensively, special teams, we've had flashes of being really a good football team, we've had flashes of being mediocre."
Gruden's counterpart in Dallas might as well be reading from the same script.
"I do think just the consistency throughout the game of execution is something that we're focused on more than anything else," Cowboys coach Jason Garrett said on Monday. "We've been in good positions the last three weeks at halftime to win ballgames, we just haven't played the last 30 minutes at a high enough level in any phase of our team."
Although neither the Cowboys nor Redskins are currently on a playoff trajectory, one of them will pull even at 6-6 going into the final quarter of the season.
In order for Washington to do that, the Redskins will have to avenge a 33-19 loss to the Cowboys a month ago at FedEx Field.
But much has changed since Dallas defeated the Redskins on their home turf.
Ezekiel Elliott rushed for a season-high 150 yards and a pair of touchdowns, fueling the Dallas offense in the win over Washington the way he did for much of the 2016 season when the Cowboys won the NFC East. But Elliott is now three contests into a six-game suspension for violating the NFL's personal-conduct policy.
With Elliott out, Dallas has dropped three straight.
Elliott's replacement, former Redskin Alfred Morris, is averaging 5.8 yards per carry. However, Morris is averaging just over 12 carries per game and hasn't topped 100 yards with Elliott gone from the lineup.
"Alfred's run the ball well," Garrett said. "He's done a nice job getting north and south and making some efficient runs for us. When given opportunities he has made some explosive plays."
Factors outside of Morris' play-making ability have limited the running back. The Cowboys have found themselves playing from behind a lot of the time in the three-game losing streak. Dallas' deficits can be partially attributed to the absence of linebacker Sean Lee, who left the Atlanta game early with a hamstring injury and hasn't played in the last two.
While the Cowboys have mostly struggled since defeating the Redskins, Washington has split four games and were competitive in losses to the Vikings and Saints.
Last week, Redskins quarterback Kirk Cousins passed for 242 yards and two touchdowns.
Even more encouraging for Washington, rookie running back Samaje Perine appears to be finding his stride as an NFL running back.
"They've handed (Perine) the ball and he's a good downhill runner," Garrett said on Tuesday. "He's physical and he's been productive for them. Very efficient in the running game and a hard guy to tackle."
Perine, along with second-year Redskins receiver Josh Doctson and kicker Nick Rose are likely looking forward to returning to their home state to face a Cowboys defense that has given up more than its share of points, yards and big plays of late. Doctson and Rose both played high school football in the Dallas area, while Perine is from near Austin.
Meanwhile, Dallas will try not to be defined by its recent failures.
"You've got to focus and lock in on each play independent of what the result was on the last play and at times we haven't done a good job of that," Garrett said. "Particularly when you have some younger guys playing, the biggest thing you have to do is put that last play behind you."