I guess since I also train in Iaido, my view of the hakama is colored by the fact that you wear one in iaido from the beginning because it is a functional part of the art's uniform. Without it my saya would not be secure. It has no meaning in terms of rank or experience.
In aikido, I voted no difference, because I think the benefits and detriments of wearing one pretty much balance each other out. For example, it does help hold my belt, but I often have to tuck it up to let students see my footwork. Yanked my toes a few times.
In our style, one starts wearing a hakama around sankyu or nikyu. Seems about right because the student has probably been training for a few years and has commitment and so the investment is not too much to ask, but also safety-wise their ukemi skills and basic movement is starting to take shape. It gives them a little time to learn how to move in one safely and be comfortable with the idea of wearing it as part of their uniform before they become a yudansha.
They also have not had to wait so long to wear one so that they attach an excessive significance to wearing one. Usually, by the time of shodan they no longer think of it as more than part of the uniform -- and that's a good thing IMO.
Often, in informal practice, I do without it.