It depends on the person how much difference they tolerate. Many do get away with wearing a contact lens in one eye after an IOL implant in the other since contact lenses do change image size less than glasses, but some have trouble so its best to be prepared since there is no guarantee. In my case I wound up getting surgery on both eyes even though my 2nd eye was still 20/20 correctible and they could barely see the start of a cataract.
After I had my first eye done I had a sense of imbalance between my eyes, though I don't know if it was aniseikonia or due to a difference in optics (a multifocal contact lens on the eye with its natural lens, the Symfony IOL in the other). I may have adapted to the difference quickly, so my data point doesn't mean much. I'd traveled for surgery so I just decided to play it safe and get the 2nd eye done instead of potentially needing to come back soon, either due to the imbalance or if the other cataract suddenly cause trouble (the first had gotten bad rapidly when it appeared).
This topic has been discussed at length. Most people cannot tolerate such differences. use the search feature and read the many informative posts. Also read this:
http://www.medhelp.org/user_journals/show/1648102/Consider-ALL-the-Options-Before-Your-Cataract-Surgery-Working-Through-Whats-Best-For-You