Sheraton is much better situated if you have any intent of sightseeing around the Cathedral, Governor's Mansion etc. I stayed at the 4Points Miraflores and enjoyed my time there; Miraflores is a pleasant and safe area to wander around. But getting from there to the historical area took a very long taxi ride.

There have been complaints that the neighbourhood around the Sheraton leaves much to be desired. I can understand that perspective - Miraflores is certainly nicer. But I personally didn't feel the area around the Sheraton was unsafe or anything. If I stay in Lima again, I'll likely stay at the Sheraton.