Breed's Hill had only one thing to recommend it over Bunker Hill - it was closer to Boston, which made it easier to fire artillery at the city. Though of course one disadvantage of this situation was that it was also a lot easier for Boston to fire back. Nobody knows why William Prescott chose the spot over Bunker Hill - it's possible that, since he was working on fortifications in the dark, Prescott didn't realize how vulnerable the hill actually was until the sun rose. By which point it was a little too late to up and move. I imagine that was probably quite an awkward moment.