to be honest, we never use a money belt or travel pouch around our necks/waists etc.
we usually carry our passports in our own small cross body messenger style bag.
a regular wallet with our usd, some aud and our passports goes with us everywhere, but we carry the bags with them at our front/to the side, rather than across your backside as most do.
we never use hotel safes, but rather take our valuables with us, or lock them in our luggage. then again, we haven't travelled very much and the places we have gone have been relatively safe. maybe our passport/money travel options will change once we have been to a wider variety of places.
in terms of how we physically carry our passports, we keep them in a waterproof, ziplock a5 size travel wallet with our flight information/tickets and transfer information.