There are many differences between a Greek theatre and an English theatre, as well as many similarities.
One of the most obvious similarities is that in both cases, only men were allowed to act on stage. Another similarity is that the plays presented belonged to two main categories: dramas and comedies. Moreover, open air theatres were common in both cases, and playwrights often achieved great fame. Finally, both used very simple props.
The differences were significant as well. In the case of Greek plays, actors often wore masks that represented the expression that they wanted their face to adopt, while these were less common in England. Moreover, Greek theatre had a stronger religious component. In the case of English theatre, entertainment was the main purpose. Moreover, in England, women were not allowed to attend plays.