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In many ways I would say safer...
I first came to Florence, Italy (a few months) and then Rome (years) as a single 25 year old girl via Los Angeles (originally from Richmond, VA). In many ways I felt way way safer in Italy (more so in Rome then Florence...), HOWEVER, if the young woman  in question comes from a small safe town where it's acceptable to leave your front door unlocked (even to just pop inside for a second) or return home late at night alone, she might need to acquire the street smarts first.
I also lived in a small small village just outside of Rome, and strangely enough (maybe in hindsight it's understandable) felt really isolated but watched by locals. Of course there are less people so they get to recognize you quickly - plus I've found Italians realllly nosey. I had a boyfriend at the time so I didn't travel  much alone, however, I probably would have safely if there was no him. And, on the same hand, now at 28, I am more cautious and probably wouldn't.
The real key :street smarts and blend in: dark clothes, don't show everything (you're not at a frat party), and avoid eye contact (insane, but if you make eye contact with men her, even briefly, it's often open season).