Dear Mr. Matt,
Ouch! That was a bit harsh.
But seriously, I believe that a good argument can be made that AH was a very old fashioned type of politician. His politics looked back to the concepts of family, honor and defernce by the common folk to their betters (but in his construct, elected by the common folk, not hereditary).
Jefferson, Madison and Burr, on the other hand, were the first modern politicians, creating a party for the express purpose of seizing control of the government (by peaceful means) and running the government in the interests of that party, perptually they hoped because their stated goal was to destroy the Federalist Party.
As modern politicians , Jefferson, Madison and Burr mobilized the masses, forged a coalition between disparate groups (Northern smallholders and "mechanics" and Southern slave owners) and enforced party discipline both in Congress and in the selection process for President. Their success in these efforts is shown by the fact that their creation survives to this day as one of the oldest, continuing political organizations in the western world.
However, as to economics and finance, Hamilton was the visionary radical and Jefferson and Madison the reactionaries. Hamilton saw a future in which America would be an industrial and financial giant with work for all and success and status based on merit not on inheriting a plot of land. He saw an America of free labor with slavery either abolished or dieing out. If all of this meant that some people would get wealthy, so much the better. If this meant that the wealthy would have a great deal of influence on government; well, in what society or time period was this not the case? Jefferson and Madison looked to an America of small farmers (and large plantation owners). They believed that commerce only meant selling American agricultural goods to Europe. They never understood banking and they hated and feared cities.
As to the question of AH becoming President if he had not become involved in the nation's first sex scandal, I believe that this was just not in the cards. Without GW's guidance and support, AH's natural tendencies to talk and write too much and to engage in many other forms of impolitic behavior would make it very hard for him to be elcted to anything except perhaps the Senate from New York.
By the end of his life, AH was convinced that he was not made for the modern American world. I believe that at least as to the political world that Jefferson and Madison created, he was absolutely correct.
Your obedient servant,
AH