Very questionable use of theories and probabilities aside, Tamicatana's question is very relevant.
Which cat? Some designs do sink, some are highly unlikely to sink and some wont.
Which mono? lose your keel
and you won't self right, get swamped, you may founder etc.
Neither mono or multi are bulletproof or idiot proof. Both can be victims of bad luck or bad judgement.
The question of which type is safer is unanswerable, it's too general for any rational discussion and sweeping views are not much use to anyone.
Any well found blue water prepared vessel of either type will survive equally well, assuming they are properly handled.
'Buttoning up' applies to both types.
Cats and tri's have ridden out cyclones, typhoons and the roaring forties where some monos haven't.
Mono's have survived despite their crews and some have disappeared without trace.
More monos have crossed oceans because they've been around longer and there are more of them.
Thousands of cats are making passages as I type this quite successfully, despite the prejudice of many naysayers.
To the OP, if you prefer living on a cat get a cat, if you prefer living on a mono get a mono.
Neither is 'safest' to cross oceans, they can both be very safe or death traps, it depends on how they are prepared and sailed.
Me, I prefer cats but I don't knock monos or the people who like them and I'll repeat, the question as put is unanswerable!