I was hoping somebody would answer this who really had done a lot of reading and research in this area recently. Darrow and Bryan worked in completely different worlds. But I am not a specialist in either of them.

But I can provide a partial answer.

First, it was a show trial in the sense that there was really very little doubt as to whether Scope would be found guilty. But it was not, in that Scopes and his defense team had made sure he would be convicted of violating the law against teaching evolution in Tennessee before the case ever came to trial.

The purpose of the Dayton trial for Scopes' team was to get Scopes convicted so the verdict could be appealed and the law itself could be challenged in the Tennessee law court. To this end, the defense wanted to raise numerous objections to the law during the trial: contending, for example, that its anti-scientific stance went against the Tennessee State Constitution's requiring the state to "cherish literature and science", and also to bring in various scientists to pronounce on the law. This ran counter to the aims of the prosecution: they did not want to get outside the matter of whether Scopes simply broke the law or not. They did not have any interest in seeing the law challenged and they resisted burdening the trial with a lot of expert testimony, which they felt would simply add to the media circus setting up tents in the town.

As has often been noted, however, the trial came at a moment when American society was changing. The rural US was threatened by the modernizing US, had reacted, and religion had been a part of that reaction. A very great audience was enthralled by the idea of conservative Christians, scientists and skeptics having a public debate. So it did force its way into the court: sometimes with general local and national approval, as when defense counsel Dudley Field Malone made an excellent speech on the need to separate religion from government. But while the prosecutorial and defense teams for the most part kept their exchanges with each other and with the judge very cordial ( Darrow was charmed by the Southern habit of every lawyer being addressed as "colonel") , the famous Darrow badgering of Bryan had a very personal quality to it that was completely adversarial, a hard-nosed somewhat cynical atheist going after someone he saw as a religious charlatan. And it was noted as such by the locals: Bryan was a hero to the rural US, and there was increased police security afterwards for fear someone might try to attack Darrow. But the judge had kept the jury away from the spectacle, likely had foreseen that Darrow mocking Bryan's theological ideas would not do anything towards establishing Scopes' guilt or innocence. So, you could say, the teams were only adversarial when it didn't matter.

There's quite a lot of secondary work on this subject ( which is why I was hoping someone with more current sources would pop up here). For the attitudes of the participants, Jerry R. Tompkins' D-Days at Dayton ( 1968) is an interesting collections of essays, five by people who witnessed or were even involved in the trial, including Scopes himself. Scopes also published a memoir about the same time ( with help): Center of the Storm, which shows that his memory was not perfectly reliable...but which shows him to have been much more than a simple science teacher. If you want to read actual trial transcripts, you can find excerpts and editions in various places online, especially of the Darrow/Bryan badgering, but here you can find the all the transcripts , the more mundane record of the trial mechanics, and see that most of the time the legal teams were not throwing fireworks.