One of the first things you learn in a reporting class is the inverted pyramid structure of an article. This means when writing a piece, you put the most important information up front. Everything that your reader needs to know should be at the beginning of the piece, ideally in the first paragraph: The who, the what, the when, the where, the why and the how.
This is followed in the next paragraph by less important details in order of importance, so it can be easily cut for length. This inverted pyramid structure is focused on the facts, the most important parts of the story that we're trying to get across to our audience.
Similarly, theater is trying to tell a story. The actors and the creative team all have the basic plot of the show that they're trying to get across. If the show is four hours or contains too much exposition, or an extra song that is unnecessary, the director and the author might make cuts of superfluous material where they can.
The facts and the basic structure are important, but the style and the humor of a piece are what keep the audience interested and engaged. A dry piece of writing does the job, it gets the point across, but people might fall asleep. The best writing is the kind that not only tells the story but does so in a unique voice. For example, an essay that is personal or emotional in tone brings a different quality to a story than a hard news piece that states the same facts.
Both theater and journalism can be taught, but only to a certain extent. The best writers and theatrical artists are born with a certain natural instinct that can't be taught-- the talent for making words flow conversationally, or a great eye for design isn't something that you can learn in school. But going to school to learn aspects of each field is an important step in developing your skills.
While I have learned a lot about rules and structure of writing different types of journalistic pieces, there is an aspect of writing that you have to figure out yourself. By reading a lot of different pieces, you learn what works and what doesn't work to make a successful piece. Read all the theater reviews that you can. Examine the structure of these famous theater critics or theatrical journals. See where the line is between stating the facts and adding your own flair. Some things that they teach you in school might not work for you, especially when the internet is changing conventions of writing. So, like with acting school, you should absorb everything that they teach you, and then decide what works best for you.
At NYU's Arthur L. Carter Journalism Institute, as undergrads we are required to have a second major if we major in journalism, presumably so we have more than one expertise than just "writing." My second major is "dramatic literature" which is basically Drama but without the performance aspect (more like an English major focused on the texts and theories).
There are many ways that I have applied my two training backgrounds together, but one that I can explain is that in writing about plays, you put the facts first. In a theater review, I find that I most appreciate the reviews that lay out the information for me, explaining what the show is all about and who the people in it are, while letting me make my own decision. In reviewing a production, if you hate the play, don't let it color your entire piece. You should be reviewing the production of this play that you hate, not focusing on spewing hate for this old play that you read in school that you have no idea why it's being revived. Focus on what is different about this production. Try to look at theatrical productions with a level head and from all sides of the story.