The question isn't as straightforward as it sounds, and it's a bee-in-my-bonnet scam that's behind it.
The top 3 in the "official" records are...
Wigan 20
Leeds 14
Saints 13
...but this is false due to some Yorkshire skulduggery.
In World War 2, at first the cup was cancelled (1939/40 season).
Then the government realised that the people working at home to help the war effort, and soldiers on leave needed some entertainment, so it was started again. But teams were allowed to "sign" any available player on a match-by-match basis. So a Wigan player could play for Doncaster if they happened to be stationed nearby. Also, someone who played in a losing team could (and did) play for another team in the next round!
Nothing wrong with this in the circumstances, but for 30 years plus after the war, these games didn't count in official records, for reasons which are clear above.
Sometime in the 70s or early 80s, when the RFL was coincidentally based on Chapeltown Road in Leeds, this changed and the wartime finals were included in official records. This was at a time when it was nip-and-tuck between Wigan and Leeds for who'd won the cup most.
Now, during the war, Leeds had access to players from the massive Catterick garrison, and unsurprisingly won the cup twice. Wigan didn't win it in the war years. Dewsbury, Bradford Northern and Huddersfield won it once each.
So the true top 3 shouldn't read
Wigan 20, Leeds 14, Saints 13....
but should be...
Wigan 20, Saints 13, Leeds 12.....just saying "for the record"
