as others have noted there are elements of vanity associated with mirrors. But that is not all of the reason, generally when one makes a decision in a story there are many things leading into the decision and the mirror is superior to a painting. The reasons follow:

1. A mirror does offer a current view of who you are, she asks it who is the fairest of all and looks at herself, but one day the mirror tells her she is not the fairest when she looks at it. This is as noted vanity, but it is also true. She is vain to ask the mirror who the fairest is, expecting the answer to be be her, but the mirror is truthful.

2. paintings do not move, a mirror moves, it is a better subject to query. You look at yourself in the mirror you move it moves, people can talk to themselves in the mirror. The painting of yourself offers the past and should stay untouched. This is why the picture of Dorian Gray does not say untouched, it behaves as a mirror, showing the truth while Dorian behaves as a painting showing the past and falsehood. The mirror is a better object to interrogate, the painting a better object to observe.

3. I believe at the time mirrors were known and more valued as objects to possess by the lower classes. This is just my belief. It is difficult for me to conceive of poor people thinking boy, I sure would like to have a portrait of me done up super fine. That would be sweet! Whereas I can totally imagine them thinking Wow, having a really large mirror would be super luxury and so useful! Damn I wish I had a mirror!!

on edit: obviously there can be many more reasons for choosing a mirror, these are just the three that immediately spring to mind if I were writing the story what I would choose.