Being that I live in London and have spent many months living in Napoli, I think that the subtle differences are important.
In London, the risk of being mugged/beaten up is a pretty one-dimensional aspect - either due to drink/drugs or simply running into bad elements at the wrong time of day in a bad area. Similar risks can be found in all urban areas the world over, including in Napoli, with low-level pickpockets, junkies hanging around the train stations looking for an easy target etc.

However, Napoli can present more of a danger than say London and other European cities on another dimension, simply due to the fact that it is in the grip of a powerful crime system. Whilst Camorristi are very unlikely to accost a tourist or even the average Neapolitan walking around, the presence is tangible and contributes to a different 'sense' of danger, which is why someone from Napoli can be said to be more streetsmart than someone in London. Walking around, knowing that the shops pay a pizzo and that all the African merchants pay up to crime bosses is simply not a mentality that I have encountered in London, where you just have to be wary for young kids who are trying to copy American hood films.