What strikes me the most here is the differences in gravitas and tragedy between the two versions of the same scene. While at their core, the same basic events occur, but their executions turn them into completely different events.
Watching the film, we know explicitly that this scene is coming, being led to it step by step. In the book, something is clearly long, but we're left with a more ambiguous dread before being whisked off to other battle scenes. Pippin is sent away and on his way to the big guns (ie. Gandalf) starts putting things in motion to delay permanent consequences. After all, he knows Faramir still lives, and has a much less regimented place within the hierarchy of the city guard.
The choice to save Faramir is not without cost, Gandalf makes a choice to save one man over helping on the battlefield. The battle still rages on, no matter the order that we come across the chapter in the text. The decision on some levels is that of visual effect - the potential loss of Faramir and the danger of corruption within Gondor make for a threat of crippling demoralization and the potential loss of the city. Fortunately for our effort, Beregond took Pippin's message seriously, holding away the servants of Denethor by force.
I don't know if it's just me, but does it stand out to anyone else that Gandalf references "the heathen kings, under the domination of the Dark Power"? I end up curious about what counts as "heathen" within the setting of Middle Earth considering the multiple (non-heathen) connected but at the same time parallel mythologies of the races. Regardless of the Christian inspiration in Middle Earth, there is certainly enough within it that Lord of the Rings has been repeatedly swept up in the moral panic that has attacked other targets such as Dungeons and Dragons (admittedly, sometimes the presence of biblical material is often used as ammunition, so maybe that's not a good example).
Denethor's death here is nothing but tragedy, the Steward lost to madness, grief, and corruption. He believes his line has been torn from him, his greatest ally an enemy, and those sworn to his service seduced away. In reality one son still lives, Gandalf still stands to defend Gondor, and those sworn to him are forced to break their vows in order to save the live of a sovereign they believe in and respect. The death of Denethor in the film however is more of a blend of accidental tragedy and comedy. Beregond has been excised entirely, and Faramir's remaining life more obvious as he twitches away from the splashing oil. Instead we get a ceremonial dousing and greeting of death, only interrupted by the 11th hour arrival of Gandalf and Pippin. On screen, we see Pippin, not Gandalf, pull Faramir from the fire, and a maddened Denethor accost the hobbit. The tragedy in this telling comes from Denethor's return to sanity and witnessing that his son still lives. The comedy comes from the almost slapstick moments of Shadowfax kicking Denethor back into the fire, and then again when Denethor runs, wreathed in flame, to fall off the spire of the city. Definitely dramatic, not lacking the gravitas the scene deserves.