The short interval since Tottenham’s wild, fun, chancy away-goals victory at Manchester City in the Champions League there has been a shared urge to draw the starkest of comparisons between the two clubs: their finances, their structure, the various degrees of faux-humble Jedi-cardigan fraudulence exhibited by their managers. It is in many ways a meaningless exercise. This is a comparison of two entirely separate things, entirely separate ways of trying to reach the same point, not to mention one that is inevitably flattering to Spurs and inevitably bruising for Pep Guardiola and the football-style soft-power project operating in the east of Manchester.

You know the drill by now. City have spent £150m on defenders in the past two seasons. By comparison Spurs ended the game at the Etihad with a pair of fishing waders at left-back and a carrier bag full of discounted supermarket meat playing defensive midfield.

Even the respective managers seem at times to present a poignant parting of the ways. There is undoubtedly a vanity project aspect to the City hierarchy’s pursuit of the Champions League. Talking about the club’s hopes in this competition at his pre-match press conference Guardiola used the word “I” or “me” 23 times in the space of 250 words. The great systems man, the great collectivist: this is still a deeply personal obsession.

Whereas throughout that second leg Mauricio Pochettino seemed lost in the night, the team, the shared effort of will. There was a moment at the end when he just gave in to it, leaping up and striding along the touchline in shiny black shirt and trousers, arms describing urgent, random, strangely sensual shapes in the air, like a high- class Mafioso hitman frantically hailing the last night bus out of Manchester city centre. Later, as the players got back into the privacy of the changing rooms, Pochettino could be seen dropping into a kind of disco-thrusting crouch and shouting “Así de grande los huevos!!”, pumping his great beefy paws and indicating, all things considered, a very big pair of eggs indeed.

Mauricio Pochettino celebrates after the second leg against Manchester City. Photograph: Marc Atkins/Getty Images

That agreeably manly, tactile quality is part of Pochettino’s charisma. He loves hugging his players. He would, you suspect, hug everyone if he could. He is in effect half bear. Above all, this seems to reinforce the sense of two extremes, of Spurs as a more recognisably human-scale project, up against the frictionless brilliance of the Sky Blue machine. No matter. It is still a false comparison; or at least the wrong one for now.

The City model – vast investment and a bolt-on Barcelona hierarchy – tells Tottenham almost nothing about what to do from here; or, indeed, about the lasting merits of one thrilling quarter-final victory.

Spurs could afford to lose Kane, and probably Pochettino. But they couldn’t afford to lose Daniel Levy

Tottenham will play Ajax next. It is a tie they could very easily lose. Not because of some craven urge to self-destruct but because Ajax are a very good team. They could also lose to City at the Etihad this weekend and find themselves struggling just to get back into the Champions League next season.

This is the immediate jeopardy of Poch-era Spurs, a club where the future is still unmade but where it feels suddenly very close at hand. And where the better comparison, the best indication of how to run this ship from here, is something much closer to home.

At which point, enter Arsenal, and a new-era launch from the past decade that offers its own far more relevant note of caution. This is the proper point of comparison, and a moment of divergence too. For the past 13 years Tottenham have been trying to become more like their neighbours. This is the moment for them to start doing the opposite, to start trying not to be like Arsenal.

The parallels are striking. Thirteen years ago, in the summer of 2006, Arsenal completed their own stadium move. Thirteen years ago Arsenal also had their best Champions League campaign, losing to Barcelona in the final, an event Tottenham have a chance to replicate in six weeks’ time.

The sense of good health was palpable but brittle. Arsenal had a star international striker linked intermittently with a move to Spain. Arsenal had a charismatic manager who was also hugely invested in the project, and were also operating under early stadium-enforced austerity. Arsenal had a visionary vice-chairman whose influence was felt in every detail. It was arguably the departure of David Dein, a year after the stadium move, that proved most telling. Arsène Wenger stayed and expanded into the space left behind. But some vital force of leadership was lost. The future began to congeal ever so slightly, helped by the arrival of ambitious overseas billionaires elsewhere.

Tottenham’s Daniel Levy is in effect the most important English person in English club football right now. Photograph: Robbie Stephenson/JMP/REX/Shutterstock

What is the lesson of Arsenal’s slow stasis in those new-stadium years, the feeling of unhappiness that eventually overtook that gleaming glass and steel frontier? Probably it is that managers are not the most important people in this very modern set-up. Spurs could afford to lose Harry Kane. Contrary to popular belief they could probably afford to lose Pochettino. But they couldn’t afford to lose Daniel Levy, part-owner, de facto director of football and in effect the most important English person in English club football right now; the only Englishman since Dein to have helped build a modern-day super club.

Tottenham’s immediate future will continue to unspool as a drama based around Pochettino, accompanied by that basic misunderstanding that his fine work can be validated only by winning the League Cup. City will remain the standard against which all teams will be judged, Manchester United and Chelsea the nearest rivals. In reality the challenge is to learn from the experience of their neighbours; to accept that for now the club is a commercial machine, one that is best run entirely to Levy’s design; and to go back to not being Arsenal.