Although your source may be white noise, and likely to stay pretty white through good electronics, what you measure with a sound pressure level meter from you speakers is almost certainly not white. Spectral level refers to level per frequency, and measures of spectral level, more likely to be measured as 1/3 octave bands, can be expected vary widely as the speaker interacts with its environment or rolls off in sensitivity.
Hearing damage occurs most at a half octave above the assault. Even frequencies to which we are not sensitive shake the basilar membrane, so high-level low-frequency sounds can definitely damage your hearing. It's not perceived loudness, but how hard the hair cells along the membrane are driven. Gun shots are notorius for damaging hearing.
So I think the answer to the OP is that for a given broadband SPL that was sourced with white noise, monitors are likely to seem louder than full range speakers that "squander" energy in the lowest octaves to which we are not very sensitive. But those of us who love pipe organs, do so value that squandered energy.
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