I'd assume the Circus Maximus was rowdier, given that chariot racing was "team" based (greens vs blues, etc), with betting evolved, and I imagine the action was a lot more exciting than the spectacle of seeing yet another public execution (death as bestias) from the nosebleed seats, or animal "hunt". During the french revolution the public executions (guillotine beheadings) sound like somewhat of a snooze-fest with the old ladies doing their knitting in the front (Les Tricoteuses).

From what I've read I wouldn't call games at the Colloseum formal, other than the senators (seated in the front) apparently having to wear togas. There were more (class-based) levels of seating, and restictions on women, but the Circus Maximus also reserved the best seating for the equestrians.