From what I've been reading on the subject, much of modern scholarship seems to discount the stories of wide ranging persecutions of Iconophiles in the empire under Leo III and Constantine V (such as the mass burnings of Icons purported to have occurred in Leo's reign, and the removal of the Icon from the Chalke Gate), while admitting that -especially in the latter years of Constantine V's reign- there was some attacks of monks and other non conformers. Aside from removing icons from churches and other public places there doesn't seem to be much in the way of changing the habits of the citizens in the period of Iconomachy. I guess I'm really asking what happened to the average Joe during Iconoclasm? What did it mean for people not of the clergy or aristocracy?
Primarily focused on the first period of Iconoclasm for this.
Sorry if that's all rather jumbled.
I'll try to answer your question, and the source for this information isn't from one or two books. It's from my university History teacher, Marc Carrier, who teaches at the University of Sherbrooke (in Québec) and he specialized in Byzantine history and the representations of the Byzantine Empire in the western world.
While you're right that both Leo III and Constantine V were both iconoclasts, the latter was a lot more intense the the former. Under Leo III, some measures were taken in order to stop iconodulism, like raising the visible icons higher so that people wouldn't reach them. After all, it would have been bady seen if he had taken to many drastic measures against iconodulism, because a big part of these people were actually women (seen as guardians of morality in the byzantine world/culture) and monks (who actually made a good part of their money by producing and selling these icons). So under Leo III, iconoclasm took more the form of debates and propaganda, which affected the people, but not so much. There could have been violences, but it was nothing compared to Constantine V's rule.
Constantine V was named "copronymus" by many people, which basically means "born in sh*t"... So you can already see he wasn't the most liked person in the world... He was raised in an iconoclast culture, and he was pretty hardcore when it came to iconoclasm. Under his reign, many iconodule women were raped in front of their family, iconodule monks were tortured (and their beards were burned on their face), and some iconophile people were taken and brought to the hippodrome, where they were ridiculed : they were ordered to spit on icons, religious women and men (monks) were forced to kiss and touch each other in front of everyone, etc.
So basically, while under Leo III iconoclast was a thing, their persecution was pretty mild when compared to under Constantine V's rule. It's not even comparable, really...
Hope this helps a little :)