To be fair, I don't think the argument is the same for both schools.
Since Aloys' most recent premiership, Brook have won it 5 times. Sure, that's not nearly as much as Kn, B & W, but it is a notable difference. Trinity's record about the same as Brook.
St. Aloysius – 1933 (joint), 1972 (joint), 1978
Cranbrook School – 1930, 1931, 1933 (joint), 1943, 1960, 1969, 1972, 1973, 1982, 1984, 1985, 1994, 2014
Since Aloys' most recent premiership, Brook have won it 5 times. Sure, that's not nearly as much as Kn, B & W, but it is a notable difference. Trinity's record about the same as Brook.
St. Aloysius – 1933 (joint), 1972 (joint), 1978
Cranbrook School – 1930, 1931, 1933 (joint), 1943, 1960, 1969, 1972, 1973, 1982, 1984, 1985, 1994, 2014