Portland has a lower crime rate than NYC in some respects. However, it appears to have a significantly higher incidence of rape compared to NYC. As for property crimes, Portland appears to have a much higher rate than NYC.

Portland | NYC crimes per 100,000 people in 2012 (FBI stats as reported by Wikipedia)
Violent crime 517.2 639.3
Murder and non-negligent manslaughter 3.3 5.1
Rape 38.6 14.0
Robbery 158.9 243.7
Aggravated assault 316.4 376.5
Property crime 5092.3 1722.2
Burglary 747.6 224.8
Larceny-theft 3745.3 1398.6
Motor vehicle theft 599.5 98.8