Had their encounter in last year's Super Bowl been in the ring, the referee would have stopped the fight after eight rounds. Both have done remarkably well to make it back to the big game, but the impression remains that the Bills are still hopelessly overmatched and will take another beating.
They will not see it that way, of course, and will draw comfort from a 30-13 victory over the Kansas City Chiefs and Joe Montana in the AFC Championship game. Montana, the Chief's quarterback, had dominated the build-up. By the end, though, he had been knocked from the game and the glory went to Thurman Thomas, the Bills running back, who rushed for 186 yards and scored three touchdowns.
Montana kept the Chiefs in contention for the first quarter but by the second it was clear that Thomas was able to generate spectacular gains and by half-time he had rushed for 129 yards. The Chiefs' last chance may have come just before the break when Montana threw an interception with the Chiefs camped just outside the Bill's goal-line.
The Chiefs did close to 20-13 in the third quarter thanks to a Marcus Allen touchdown. By then, though, Montana had been knocked out of the game by Bruce Smith and the Bills held on for a comfortable win.
After four successive AFC championships, the Bills are entitled to a sense of great achievement. They know, however, that after the thrashings they have encountered at the Super Bowl in the last few years, many were dreading their reappearance there. A placard at the Chiefs game read 'We're Back. Deal With It America'.
This was fair enough, but they will now have to deal with a rampant Dallas team who trounced the San Francisco 49ers 48-14 in the NFC Championship game.
The game hinged on the second quarter. The 49ers drew level at 7-7 on its first play, but the Cowboys then scored three unanswered TDs to take control, the second following a Thomas Everett interception of a Steve Young pass.
The 49ers made something of a rally in the third quarter and knocked Troy Aikman, the Cowboys quarterback, out of the match. But after a shaky start, Bernie Kosar proved a move than capable deputy and the Cowboys became NFC champions for the second year running.
The Cowboys said yesterday that Aikman, who sustained a concussion and spent the night in hospital, was expected to be fit for the Super Bowl.
In the build-up to the 49ers game their head coach, Jimmy Johnson, had guaranteed the Cowboys victory, apparently hoping to provoke a positive reaction in his players. He is unlikely to do the same this week, but another triumph on Sunday seems a formality.