Jefferson and Jackson had very different ideas in regards to who should participate in the governance and to what extent.
Up until Jefferson's time, the dominant belief was that the wealthy should govern as they were best qualified, better educated, and had more experience managing power. Jefferson contradicted these thoughts to a certain extent, expressing that any man that could support himself without relying on anyone else, should be allowed to participate in the government and election process. This only included people who were self-employed and thus their vote could not be influenced by anyone who controlled their livelihood.
Jackson, on the other hand, had a more extended view. To him, any free, adult, white male should be able to vote regardless of how they made their living (only leaving out women, slaves and native americans). Jackson believed that this way, the majority's opinion would be able to decide the country's future and this would always lead in the right path.
Hope this helps!