He was an anti-crime mastermind, but more so as far as cracking down on organized crime. I think, as crude as it might be to say, that things such as abortion, mass incarceration and the increase in cost of living in New York, probably had more of an impact than anything on NY crime, statistically speaking. The populations which had the biggest numerical impact on contributing to crime, decreased in number due to being put away or having to move away. Less kids were also being born to troubled circumstances.
However, even the mob bosses themselves admit that Giuliani was a bloodhound and definitely had a big impact on putting many of their major figures behind bars, by maximizing the application of RICO laws and such. But much of their crime wasn't something that wasn't going to be shown in the statistics, anyway, as it was mostly financial crimes, loan-sharking, protection rackets, corrupting unions, running illegal gambling operations, blackmailing, etc. so taking down the mob is not really the reason why New York's statistical crime decreased so heavily. It probably did make life a lot easier for a lot of smaller businesses and such, though, as they no longer had to deal with mobsters getting a cut from all of their activities.
