I'll put this up front: The Chiefs need it more because they're more likely to be a player in the AFC race. You can find Buffalo Rumblings response to this here.
Both teams are 5-3 and both have somewhat difficult schedules down the stretch so this game is obviously extremely meaningful to both teams. Any argument I make in favor of the Chiefs, Bills fans can probably make in favor of the Bills. In fact, three of the Bills final four games are against the Broncos, Packers and Patriots so they need to keep winning to prepare themselves for what very well could be three losses in the final four games.
But this is a Chiefs blog and we care more about the Chiefs, who currently hold the sixth playoff spot.
The Chiefs schedule the rest of the way includes a handful of teams that are going to be vying for a playoff spot in the AFC, including the Bills, Broncos, Steelers and Chargers. The Chiefs also play tough NFC teams the Seahawks and Cardinals. There are also two game against the Raiders which should be wins (but now you know the Chiefs are going to beat the Seahawks and Broncos and lose to the Raiders twice because that's just how the NFL works).
That's a tough stretch of games. They're all important but those games against AFC contenders the Bills, Broncos, Steelers and Chargers look like the most important for tiebreaker scenarios. The Chiefs can help themselves out immensely by beating those teams, improving their conference record and owning the head to head tiebreakers.
There are an NFL record 11 AFC teams above .500 right now. How important do you think tiebreakers are going to be? Very, very important. That's why this, an AFC game, is so important.
I say this with all respect to Bills fans but I believe the Chiefs are more of a real contender than the Bills. Both are obviously not Super Bowl favorites but I believe the Chiefs are better suited to compete in the playoffs than the Bills are right now, especially considering Kansas City was just in the playoffs last year. So Kansas City, because they're more likely to make noise down the stretch, needs this game more than Buffalo.