Rudy Giuliani rose to prominence as a US Attorney going after white collar, mainly high-visibility Wall Street "crime". No doubt this was part of his political plan (nothing wrong with that), EXCEPT that his famous prosecutions which won him the Mayoralty of NYC (which is a bigger and sharper-elbowed organization than many state governments in the US) ended in reversals after years of appeal - after ruining countless lives and careers and marriages, including some folks I knew.
His career was built on fear. When the US Attorney decides to target you, good legal advice is to get down on your knees and pray, because once they have invested some time and money in you, they will be highly motivated to find some way hurt you, no matter what.
Thus, around NY, he is viewed as dangerously ruthless and calculating. Maybe fight fire with fire, and run him against the ruthlessly calculating Hillary. Nice people.
His case against Michael Milken was the most famous of many. People forget that Milken never broke any existing known laws other than the law against getting rich. No, new theories, versions and extensions of law were invented for Rudy's prosecutions. Milken, a financial genius and, in my opinion, probably an honest man, spent two years in jail for nothing. And now his invention, Junk Bonds, are a major capital market, fueling all sorts of growth in our economy.
Rudy is a likeable, charismatic fellow, a true conservative, and he did us all the favor of rescuing NYC from the mess it was in long before the WTC. At the time, the newspapers had been saying that NYC was ungovernable. I would vote for him against any Dem, but I do not respect him. I suspect that he has the heart of a Brooklyn thug. I still feel upset about the lives he destroyed. Maybe that's just politics, life in the big city, etc., but I'd rather not think so.
He of course also deserves credit for his handling the attack on New York, but I swould have expected nothing less of him and would never imagine him going Nagin. Still, his real achievement was bringing Democratic NYC back from decay and anarchy via conservative principles, firmness, persistence, and good cheer.
If you haven't been to NYC recently - go, and see what Rudy - and now Bloomberg - have accomplished.
For the whole story of his Wall Street prosecution days, the Journal of Libertarian Studies has an excellent summary. (I forget how to quote from PDF files.)