I can't answer that question for Italy, but depending on the location, theft / petty crime is either an ongoing problem or a rare and unusual event.
Certainly important to be aware of where you are, as some locations present easier opportunities. A very different risk walking the vineyards on the Langhe or even the coastal walks of Cinque Terre to the bustling streets of some city based heavily touristed locations.
Having two phones, both with GPS tracking enabled for the other one, might be worth considering if in a bustling city where there will be thieves and police.
The act of taking a photo is a clear advert to a pickpocket/thief that we're tourists with a camera/phone/tablet that might be worth stealing. I have to say this makes me more wary in busy cities, and as a result I doubt I've ever taken a photo in a bustling location. Apart from that, although I'm not a regular photo taker these days, I rarely find myself in locations that would give me concern.
As with money, it's worth thinking it through to know your strategy for prevention and mitigation. Having an older camera could help both of these, but so could ensuring where you stand reduces the chance for someone to make a quick snatch for the phone without attracting the attention of a travelling companion. Having a safe place to put the phone after use would be just as important. The more bustling the location, the more thought I would give to that strategy, but in the normal low-risk areas, I give it no more thought than I would do at home.
