The second similarity is that both movies are devoted to "show don't tell."
Die Hard obviously already has a leg up here, being an action movies. Action movies, by default, are reckoned to focus more on show than tell. Still, even in comparison to later Die Hards, the movie is commendably free of forcing ideas or character development onto the viewer. Alan Rickman's character is never diagnosed; he simply is. Likewise, while Powell eventually explains his demotion (why he is driving around in a squad car answering routine calls) to McClane, the character's essential personality is already well-established. Likewise, although McClane's wife knocking over his picture proves a lucky plot point, it is also entirely within character.
In addition, all the bad guys have distinct personalities without anyone ever pointing this out.
Likewise, Topsy-Turvy is entirely free of editorial comments. The most basic comment is that Sullivan without Gilbert (and Gilbert without Sullivan) were never as good as their supporters might have claimed. (The two men themselves were well-aware of their "joined at the hip" success.) In the movie--and on the CD--this is made apparent through the music. Nobody ever says, "Boy, Sullivan, your 'Broken Cord' sure is popular, but it in no way compares to any of The Mikado's music," mostly because, at the time, nobody believed this. "Broken Cord" was a hugely popular Victorian song--and one of Sullivan's sole efforts that made him immensely wealthy.
In Die Hard, a great "show don't tell" scene occurs when the FBI helicopter gets blown up. "Well," says Powell's captain, "We're gonna need some more FBI guys, I guess."
At this point, the captain has demonstrated exasperation with Powell, who tells him off; exasperation with McClane, who tells him off, yet all of his exasperation is in keeping with his fundamental personality of dry irritation. So he gets one of the most memorable lines in the film--because he is the character who would say it.
In the scene, Gilbert and Sullivan are at odds; Gilbert is producing the same type of plot/lyrics as ever; Sullivan is sick of them and feels pressured by his friends to do something "serious." Both men are contracted to the D'Oyley Carte Opera Company to write more operas together. D'Oyley Carte, a smooth operator in his own right, has tried speaking to both of them, specifically Sullivan. Now he turns the matter over to Lenoir who takes his desk while Carte sits on a nearby couch. Both Gilbert and Sullivan are present. Lenoir speaks bluntly yet diplomatically to both of them. She lays out the problem. Nobody will give in:
Gilbert: Every theatrical performance is a contrivance by its very nature.Carte is upset at the "offense" to Lenoir "(Gilbert mentioning prostitutes). Gilbert apologizes. Lenoir waves away the "offense" as immaterial. She's a businesswoman. She wants a resolution. There is no resolution. Everyone very politely bids each other adieu, Gilbert and Sullivan collecting their hats.
Sullivan: Yes, but this piece consists entirely of an artificial and implausible situation.
Gilbert: If you wish to write a Grand Opera about a prostitute, dying of consumption in a garret, I suggest you contact Mr. Ibsen in Oslo. I am sure he will be able to furnish you with something suitably dull.
It is an amazing scene because it digs to the root of the two men's disagreement, yet remains absolutely civil. It is fierce conflict clothed in dialog, all of which is conveyed without misstep by the involved parties.
Show me, don't tell me--I can fill in the rest.