Chicago Fire: New York Jets - The Fire and the Jets actually have more similarities than you think. The Jets won Super Bowl III, the Fire won the third MLS Cup. They both are one-trick ponies when it comes to chants ("Fire" vs. "J-E-T-S! Jets! Jets! Jets!" ad nauseum). And while the Jets are in line to make the playoffs this season, they were hot garbage for the past few years - just like the Fire.
D.C. United: Pittsburgh Steelers - Both the Steelers and United won a bunch of championships a long time ago, and both fan bases are eager to remind everyone of how great they used to be. Both teams are decent enough now, but can't seem to make it over the hump and get another championship to rub into everyone's faces
FC Dallas: Arizona Cardinals - Both teams have squandered their lone chance at a title, and both teams are decent enough every once in a while to win the division (however both are more often than not subject to a mid-season swoon that all but kills any and all playoff hopes).
LA Galaxy: New England Patriots - Both teams are synonymous with winning, and both are universally reviled by fans of every other team in their respective leagues. Bonus points: both Bruce Arena and Bill Belichick would slit your throat and not think twice about it if it meant getting a leg up.
New England Revolution: Minnesota Vikings - Sure, everyone goes with the Buffalo Bills comparison so I'll go with the Vikings who also lost four Super Bowls. Unlike the Bills however, both the Vikings and Revolution have turned into not-so-terrible teams.
New York City FC: Jacksonville Jaguars - Both teams have been completely mismanaged since the beginning, both teams aren't even the favorite in their own city, and both have their futures inextricably linked to England.
Philadelphia Union: Detroit Lions - Both teams have been the definition of futility, and both have been run by General Managers with positional fetishes: Matt Millen loved his wide receivers as much as Nick Sakiewicz loved his goalkeepers.
Portland Timbers: Carolina Panthers - Once an afterthought in their respective divisions, the Timbers and Panthers are seen as the team to beat. If the Panthers win Super Bowl 50, the comparison will be complete.
Real Salt Lake: Saint Louis Rams - Remember when these teams were good? It wasn't all that long ago, but it sure seems like it. Once dominant teams now relegated to being where you look for fantasy sleeper picks.
San Jose Earthquakes: Oakland Raiders - These teams have a history of relocating and were powerhouses back in the day with legendary swagger that have been reduced to hollow shells of their former glory. The only thing scary about these teams now are their fans - and not in a good way.
Seattle Sounders: Indianapolis Colts - Both the Sounders and Colts roll through the regular season only to fall flat in every postseason. The championships won by both teams (the U.S. Open Cups for the Sounders and the Colts' Super Bowls in 1970 and 2006) seem like such a long time ago when tempered against coming so close so often.
Sporting Kansas City: Seattle Seahawks - Both teams benefited greatly from rebranding, having only a couple of decent seasons before ditching old uniforms and color schemes. Also, has anyone ever seen Brian Bosworth and Jimmy Nielsen in the same place at the same time?
Toronto FC: Dallas Cowboys - Not the Jimmy Johnson era Cowboys or even the Tom Landry era Cowboys, but the post-1990's Cowboys that overspend and can't seem to win a playoff game on the rare occasion they make the playoffs. This also makes Michael Bradley the equivalent of Tony Romo.