Most recent scholarship suggests Burr would have been quite good. The only reason he has a bad history, is the trumped up treason trial and his reclusive life style after the trial. Burr had no direct living descendants, unlike Jefferson and Adams who had plenty of opportunities to make themselves look better to posterity, as well as relations to cover up for them.
I think a Burr presidency is more Hawkish than Jefferson, and may lead to some sort of earlier Embargo act, which will be ruinous for the economy. I would hope that a President Burr would stay out of European affairs but I think the he will be drawn in on the French side. Burr who is just as astute as Jefferson will snap up Louisiana if it is possible. Burr will more than likely support the bank. We will still see the Amendment to the EC process. The only reason Burr lost is because Hamilton feared a Burr Presidency more than a Jefferson one. Most Federalists wanted to vote for Burr, so all Hamilton needs to do is stay quiet and release the reps.
While I am consider myself an ardent Hamiltonian and defender of the "Little Lion" as much as anyone on this board. I think He missed the boat here. Burr was an erudite and capable man who had lacked the patronage of Hamilton and family connections of Jefferson, to move up the colonial ladder. The reason both (yes Both , why do you think Jefferson dropped him in 1804, the duel was only part of it, he would have been dropped anyway) considered him a threat is because he was just as smart as they were and just as capable.
I think a Burr Presidency will Federalist in policy, increased centralization, hawkish foreign policy; but D-R in rhetoric. He supported manumission and abolition as well as woman's rights, I doubt you will see movement on these, because Burr was an astute politician and a decided pragmatist.