Do not talk to Tottenham Hotspur fans about the club's capacity to fall short. Whether it be down to meat-based Italian pasta dishes or the scarcely believable sucker punch from a cross-town rival, they have seen their goal in recent seasons wrested from them in cruel and faintly ridiculous fashion.

This time round, the battle for Champions League qualification has again come down to the wire and there is an apprehension underpinning the excitement at White Hart Lane, the fear that fate could deal them a new and devilish card. If André Villas-Boas's team beat Sunderland at home on Sunday, they would finish on 72 points, which would be a club high in the Premier League years.

It is a haul that, almost always, is sufficient for a top-four place. Only once since the league was slimmed down to 20 clubs in 1995-96 has the team in fourth taken more than 72 points: Liverpool finished with 76 in 2007-08. Villas-Boas brought up the statistic on Friday morning. It is on his mind. But 72 may very well not be enough.

Over at Arsenal, they know what they need to do and they intend to do it. Win at Newcastle United and they would ensure qualification to Europe's elite competition for the 16th season in succession. Tottenham, as they were last season when Chelsea won the Champions League to relegate them to the Europa League, despite a fourth-placed finish, would be powerless, consumed by ifs and buts.

This is what Arsenal do. They finish in the money places and, also, they finish above Tottenham. They torment Tottenham. Never in Arsène Wenger's 17-year tenure have Arsenal trailed in behind their neighbours. The last time it happened was in 1994-95.

It was perilously close in 2005-06, when Tottenham entered the final day one point ahead of Arsenal in fourth. But then the majority of their team woke up with gastroenteritis or, according to folklore, a stomach bug from a dodgy lasagne and they did not have the strength to win at West Ham. Arsenal beat Wigan Athletic and laughed loudly.

Arsenal retain the hope of a third-placed finish, although they need Chelsea to slip up at home to Everton and there is the 130-1 shot, according to bookmakers, of an unprecedented play-off between the London clubs for the third and final automatic pass to the Champions League group phase. That fixture would take place at Villa Park on Sunday 26 May and would be needed if Chelsea were to draw against Everton and Arsenal won by one at Newcastle, scoring two more goals than Chelsea in the process. This would see the clubs inseparable on points, goal difference and goals scored.

But Sunday's entertainment essentially boils down to Tottenham versus Arsenal; to the quest for each club to force themselves on to the right side of the finest of margins. Every other major issue in the division has been resolved. The spotlight on north London promises to be intense.

There was common ground between Wenger and Villas-Boas. The former noted how Arsenal had already equalled their 70-point tally from last season, despite the various problems that they had encountered, chief among them the demoralising departure of Robin van Persie to Manchester United, and he said that "I will keep fantastic memories of this team".

Villas-Boas reflected a little wistfully on the clutch of recent draws and the 2-1 loss at Everton in December, when his team conceded twice in the last minute. "The Everton defeat was the real mark on the season," he said. But he professed himself to be "extremely satisfied" with how his debut campaign had gone. "We always look back with the sensation that we've done things properly," Villas-Boas said. "But it's not up to me to judge."

The judgment will come on Sunday evening and, for Arsenal in particular, it is hard to escape the feeling that it will be black or white. Even Wenger acknowledged that the financial consequences of missing out on the Champions League would be "big", although he maintained that the sporting reasons would be the most painful.

As he prepared for the fixture against a Newcastle team still basking in the relief of avoiding relegation at Queens Park Rangers last Sunday, there was the narrowing of focus that has characterised the recent weeks for Arsenal. And confidence. Wenger positively brimmed with it.

At the beginning of March, after Arsenal lost the derby at White Hart Lane, they trailed Tottenham by seven points. Villas-Boas claimed that Arsenal were "in a negative spiral and once you get into that negative spiral, it's difficult to get out of it". The words ring hollow. Arsenal have since been unbeaten, winning seven and drawing two in the league. They even won at Bayern Munich immediately after the derby, even if it failed to prevent an away-goals exit from the Champions League.

"This team suffered for a very long time from a lack of confidence because you take the talisman away – Robin van Persie – and get new players in," Wenger said. "Then you lose the first big games and suddenly, we are faced with scepticism. Balancing the team took a while but since this has been back we have been very efficient. The Bayern Munich away game was very important. You could feel after that we could do it.

"I had the feeling it could go to the last day and when we were seven points behind, we'd have been happy for that. But we've fought back to be in a position where we can master our own fate. We know how to behave to win. Let's just continue what we've done recently."

There were forward glances from both managers, inevitably, concerning personnel upgrades. Villas-Boas spoke of his desire to appoint a technical director to oversee player transfers and he admitted that he had tried to sign the Barcelona striker David Villa last season when he was in charge at Chelsea. Villa is a possible target for him again this summer.

Villas-Boas also said that with José Mourinho set to return to Chelsea and be afforded the money to make a huge impression on the market, the west London club would "absolutely be the team to beat" next season. Tottenham, he suggested, had to try to keep pace.

It tends to feel more cerebral at Arsenal and Wenger's reflections on Sir Alex Ferguson, the outgoing United manager, carried an unwitting subtext. "He never looked like he refused to move forward and be open to new things," Wenger said. "You have to respect this progressive attitude. We can all be a little bit restricted to our experience and what worked before."

Wenger has regularly stood accused of the above and his revelation that he was close to signing the free agent and France Under-21 striker Yaya Sanogo from Auxerre sounded like something from the tried and trusted.

It was difficult, though, to look too far beyond Sunday's showdown, when the passions will rage and the drama swirl. "It's one of the biggest rivalries in football," Villas-Boas said. "The buzz that you feel around the club now and the pressure is extraordinary."