How are Greek tragedy and modern drama alike?
The first difficulty here is that Greek drama consists of both tragedy and comedy, as does modern drama. Thus it would make more sense to compare Greek drama with modern drama or Greek tragedy with modern tragedy. As phrased, it's rather like asking someone to compare apples with vegetables.
All drama, both Greek and modern, operates primarily as a form of mimesis, in which rather than having a narrator tell a story, actors appear on a stage and pretend to be the characters being portrayed. Mimesis imposes technical limitations, usually, in both Greek and modern drama, restricting the scope of time and space that may be portrayed. Since drama is a form of live performance, and one cannot, as it were, pick it up and put it down at one's convenience, the length of a performance is limited by the attention span of an audience.
Both ancient and modern drama are performed in theaters or designated performance spaces.