The reason why I mentioned the Bronx being slightly more dangerous than Brooklyn is because although Brooklyn may pump out more violent crimes annually, the higher population, the fact that there are more low crime nabes in Brooklyn than the Bronx, on top of the steady gentrification wave that's taking place helps "soften the blow" if you will, on the borough's crime rate.
The Bronx on the other hand has a much lower pop (1.4mil BX vs 2.6mil BK -- almost half), but nearly the same number of violent crimes per year (I would estimate it around 60-70% of BK's numbers). Also there are less low crime areas in the BX, and even those areas are starting to decay (Van Nest, Morris Park, Bedford Park, Kingsbridge, parts of Throggs Neck, etc) so crime is more widespread.
In addition, the Bronx is seeing an influx of of poor residents and immigrants while the the yuppification of BK is intensifying. So in essence, if by dangerous you're going by just the body count, then Brooklyn wins, but if by dangerous you're going by the likelihood of you being a victim of a violent crime, then I would give it to the Bronx. Just wanted to clear that up.