Spurs finished above Arsenal last season and while Giggs sees Pochettino as possessing the best squad at the moment, he still believes that they have some way to go before coming the true dominant force in North London.
Arsenal lifted the FA Cup in May, their third time winning the prestigious trophy in four years.
Arsenal lifted their third FACup in the last four years with victory over champions Chelsea at Wembley in May, though, and ahead of this weekend's north London derby Cech insists Spurs need to secure silverware before they can claim to have moved ahead of their rivals.
'There is always one odd year where things can change, but the most important thing for us is competing against the other teams for the Premier League title and for the glory.
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He went on to further tell Sky Sports.
Despite talk about the continuous failings of Wenger and Arsenal, the Gooners have still won the FA Cup 3 out of the past 4 years.
The first North London derby of the season kicks off on Saturday when Spurs travel to the Emirates in the first Premier League game after the global break ends.
'There was always something missing but I would say the difference was when Pochettino came, ' the 35-year-old from Czech Republic added. Their last UEFA Champions League campaign prior to this season was very uninspiring and disappointing, but they've made some major noise this year. Two years ago when we finished above them we were disappointed because we didn't win the title.
The Gunners' form has been patchy, especially away from home, and it's hard not to draw some parallels between that and the fact their two star players, Alexis Sanchez and Mesut Ozil, have yet to make the kind of contribution you'd expect from players of that talent.