This answer only talks about Jackson himself. I think that there is a distinction between Jackson the person and Jacksonian Democracy as an idea and as the distinguishing feature of an era.
Whether Jackson himself was power hungry is in some ways irrelevant. Jacksonian Democracy as a whole was very democratic if you were a white man. It was based on the idea that all white men should have the right to vote and the ability to participate in politics.
Of course, for a person of color or for a woman, this was not a democratic time. These groups had very little in the way of rights.
Overall, then, regardless of Jackson's personal attributes, Jacksonian Democracy was very democratic for its time. It was the era of universal white male suffrage and power for the "common man." This was much more democratic even than the US had been prior to this era.