Jefferson had noble ideals, which he did not always live up to. Andrew Jackson didn’t even have the high ideals; when it came to Native Americans and African slaves, he was an unrepetant bigot.
Jefferson was in theory opposed to slavery but felt he couldn’t afford to give up his slaves. He also believed that Native Americans were in theory equal to Europeans, and should be given equal rights, but only after they were re-educated in the Western fashion. Jackson just believed in slaughtering them.
One thing they both agreed on was opposition to any kind of wealth requirement for voting. This may be hard to believe today, as there are now several Constitutional amendments in place guaranteeing the right to vote to every adult citizen.
But 200 years ago, this issue was a big controversy. Hamilton and John Adams were both strongly convinced that it was right and proper to require each citizen to own a certain amount of property before they could vote.
Ironically, the Republicans of today seem to echo Hamilton and Adams by wanting to make it harder for poor people to vote. Supposedly this issue had been settled by the time Jackson came into office. (Although votes for non-whites and women had yet to be won.)