He initially said big games "with something big on the line". Kane has rarely been in that position, because Tottenham rarely have something big on the line. If we're counting league games, Kane scored plenty against big teams in the league last season, but they were nowhere near title contenders. If Tottenham were league contenders, then you could class his "big game" record as similar or better than Haaland's based on form in the league.
Edit: I don't think Haaland scored against Bayern in Germany either; arguably the big game in Germany. Think he popped that cherry in preseason last year when he joined City. Not saying he's bad or anything, but it's been a bit of a thing.
Haaland at City against the other big 6 in the league:
6 goals and 4 assists in 9 games: 0,67 G/90 and 1,11 G+A/90
Haaland was anonymous in the finals for City last season, but he still scored 7 and assisted 1 in the KO stages of the CL for City last season and a hattrick in the QF of the FA Cup. He was anonymous because their opponents put 2 guys on him at all times.
Kane against the big 6 in the league last season: 6 goals and 1 assist in 10 games: 0,6 G/game and 0,7 G+A/game (could you class this as similar or better than 0,67G/game or 1,11G+A/game?)
Regarding Haaland in Germany:
- He scored 5 and assisted 1 in 391 minutes against Bayern for Dortmund: 1,15 G/90 and 1,38 G+A/90
He was almost allways good against them, they just couldn't beat them.
- Haaland against other "big teams in Germany" for Dortmund (Leipzig, Leverkusen, Wolfsburg and Gladbach): 19 goals and 3 assists in 19 games, or Frankfurt and Hertha: 8 goals and 4 assists in 8 games....
- Haaland in KO stages in the CL for Dortmund:
6 goals and 2 assists in 540 minutes against (PSG, City and Sevilla): 1,0 G/90 and 1,33 G+A/90
- Haaland in the DFB final against Leipzig: 2 goals in 90 and won threm the trophy.
He also scored in both the games they were knocked out of the cup in the years they didn't win.
Kane on the "big stage" through out his career:
Kane in KO stages in the CL:
2 goals and 0 assists in 7 games: 0,30 G/90 and 0,30 G+A/90
Kane against the other big 6 teams for Spurs:
42 goals and 14 assists in 94 games: 0,45 G/game and 0,60 G+A/game
Kane in the FA cup matches Spurs have been knocked out were he started:
2012: 5th round at home against Bolton: 0 goals and 0 assists / 0 - 2 loss
2013: 4th round at home to Luton: 0 goals and 0 assists / 0 -1 loss
2016: 5th round at home to Crystal Palace: 0 goals and 0 assists / 0 -1 loss
2017: Semifinal against Chelsea: 1 goal and 0 assists / 4 - 2 loss (did nothing in the QF)
2018: Semifinal against Man United: 0 goals and 0 assists / 2 - 1 loss (didn't play the QF)
2021: 5th round against Everton: 1 goal and 0 assists / 5 - 4 loss on penalties (subbed off at 67')
2022: 5th round against Middlesbrough: 0 goals and 0 assists / 0 - 1 loss
He hasn't helped Spurs to get deep in the FA cup once.....
Kane in the League Cup exits and semifinals:
2015: Semifinals against SU (1-0/2-2): 0 goals and 1 assist in 2 games
2015: Final against Chelsea: 0 goals and 0 assists / 2 - 0 loss
2019: Semifinal at home against Chelsea: 1 goal and 0 assist / 1 - 0 win (he didn't play the return match and spurs lost)
2021: Semifinal against Brentford: 0 goals and 0 assists: 2 - 0 win
2021: Final against Man City: 0 goals and 0 assists: 0 - 1 loss
2022: Semifinals against Chelsea: 0 goals and 0 assists / 0-2 and 0-1 losses
That's a grand total of 3 goals and 1 assist in 15 important domestic cup games for Spurs, and they won 0 trophies.
You could bring up his England record in championships and important games as well:
Euro 2016: 0 goals and 0 assists in 4 games (lost to Iceland (!!) in the round of 16)
WC 2018: 5 goals (2 pens) against Panama and Tunisia in the group stages, 1 goal (a pen) in the round of 16 and 0 goals and 0 assists in the QF, SF and 3rd place final.
Euro 2021: 0 goals and 0 assists in the group stage, 4 goals in the round of 16, QF and SF and 0 goals and 0 assists in the final (best tournament of his career, but went missing in the final)
WC 2022: 0 goals and 3 asssists in the group stage, 2 goals in the round of 16 and QF (knocked out against against France in the QF)
Nations league: 3 goals and 4 assists in 18 games, including 0 returns in the finals in 2019.
Total: 15 goals and 7 assists in 40 games in championships and NL. 7 goals and 0 assists in 13 KO games
Kane's record in "big" games is not remotely similar, and miles upon miles away from being better.