It's definitely safer in Kenmore Square. There are homeless there, but it's also home to thousands of Boston U. and Northeastern students. BU owns most of it. It's mostly dorms and frat/sorority houses and Northeastern owns "the towers". It's also right on the Charles River and a block from Fenway Park.
Parts of Back Bay are safe, but it's also home to one of the city's largest homeless shelters, housing projects, and gangs. I went to college in Back Bay and watched a guy get murdered right at the steps of the Boston PD station there (Area D). He got stabbed about 20 times before enough cops could get out of the station to break up the fight and get to the victim (gang related, about 20 people involved). They'd chased him out of the housing projects about a block away. My college was right across the street, it all happened as I was sitting in a window overlooking the street in front of the police station.
That's my take on it anyway. I grew up in Boston. I also worked as an EMT in Boston and we spent every free minute hanging out in Kenmore Square because all the girls and clubs made it a fun place. We called it Hollywood. We never went out of our way to park the ambulance in Back Bay. But in all fairness, I never really felt unsafe in Back Bay, either. I stayed away from the projects so didn't have any problems. I'm originally from Mattapan so as a native, Back Bay was a walk in the park.