I currently live in puglia, with my partner and two children. The first thing i can say i feel safer living and walking the streets near to where i live, than i do in the UK. There is no pub culture, as it is frowned upon by the italians, and hence no violence.
Since moving to puglia we have had our fair share of bad luck, but with the support of the local people we haveover come this. In general you can't get away from thefts, but these are mainly done by oppotunists and in the countryside, in the winter when the countryside homes are not generally used so much. In the towns, where i am i have never heard of any trouble, and would class it as a trouble free, quiet place to live.
Cities in general have a different feel. Like they would in UK, but in general they are civilised. I don't know of any organised crime, but as many italians tell me, the organised crime is still present, but mainly in the cities and if you own a business. When it comes to people from the Uk you wouldn't know it existed unless someone told you about, or affected you in some way, due to the enforced mafia law.
There is so much i could say about living there, but a post here wouldn't do the area or it's people any justice. But anyone thinking about full time relocation i would definetly recommend puglia as a place to settle down,relax and feel at peace. And as my children say they wouldn't live in the UK unless they really had too, bearing in mind they are 6 and 8 years you can't knock them for taste and telling the truth.
Hope this gives a little insite.