“In what way were they different and how is that relevant?”
Pagan religious ceremonies were an integral part of the program. That is VERY relevant.
An additional problem is that a common feature of the circuses (not the theaters) was gladiatorial games in which the gladiators fought to the death. I’ve seen sources that indicate that Jews were in at least some cases encouraged to attend these horrible events in order to plea *en masse* for the gladiator’s life, as it was often the sentiment of the crowd that determined the fate of a defeated gladiator. Unfortunately, many Jews were enslaved as gladiators by the Romans after korban bayit sheni.