They appear to share superficial similarities. What Ive heard about ancient warfare seems to place emphasis on morale and shock, with missile exchanges and short clashes mutually broken off, rather than a charge and constant melee combat as per hollywood.
Now, I can't really speak to any ancient warfare and how it occurred.
What I can say is that in works like The Crowd in History by George Rude is that most "mobs" do not act with the aimless violence that are often portrayed in popular literature/cinema.
These mobs tend to have specific goals and reasons for coming together and have certain things they are willing to do and things they are not. For example, in food riots in England during riots, mobs would sometimes force vendors to sell their products (bread, grain, etc) at what they thought was a fair price, instead of just taking it.
This idea of the "Moral Economy" was later coined by historians like E.P. Thompson and is now much discussed.
So, to get back more to your question, yes there were short clashes with breaks, speeches, negotiations, counter negotiations etc. Riots are not usually all out violence and tend to ebb and flow with the events and even the time of day.
I'm not exactly sure how it corresponds to ancient warfare, but I assume it depends on what ancient warfare we are exactly talking about.