Depends on who you ask from that time. To come at this question from a different angle than the above posts, if you asked the Five Civilized Tribes sent on the Trail of Tears, they would argue Jackson was distinctly undemocratic. The Supreme Court of the time, which ruled the Indian Removal Act was unconstitutional, was ignored altogether by Jackson, who removed the tribes anyway, so I would guess the Court would say there wasn't much democracy in Jacksonian Democracy.
While the phrase refers to Jackson's specific approach or philosophy of government as it compared and contrasted to earlier interpretations such as Jefferson's, the obvious hypocrisy of his actions, to me, makes the phrase a serious misnomer.
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.
Andrew Jackson had a strong personality, a characteristic revealed by his nickname "Old Hickory", the toughest of America hardwoods. He brought this tough character to the American Presidency and stressed his individual authority which was often at odds with Congress. He used his right to vetoe Congress legislation more than all the previous Presidents put together. Jackson also opposed programs to make society more democratic such as educational reforms and freedom of religion. He also began the deportation of the Cheerokees along the Trail of Tears. As he was both the leader of Democratic Party and the President, Jackson concentrated an unprecedented power in a single person.