I would like to know if there is any difference between (1) and (2).
(1), Now that I've grown up, I realize how important it was.
(2), Now that I've grown up, I have realized how important it was.
Re: realize/have realized
(2) is unnatural in this case, since you have just mentioned 'now', placing the action of 'realizing' squarely in the present. To make (2) natural, change it, for instance, to:
(2a) Since I have grown up, I have realized how important it was.