Previously on "NuWho episodes that make a lot more damn sense when you realize which classic serial they're ripping off": Utopia, Genesis of the Daleks, and Malcassairo as RTD's remix of Skaro. Now, Utopia comes off pretty badly once you set up the comparison--the Futurekind are dumb, dumb, dumb next to the Mutos, for example--but that's mostly because Genesis is fucking flawless. We're still dealing with some of Rusty's best work, which appears to be paying homage to some of the classic series' best work. What do you get when Rusty recycles a bunch of techniques from an ambitious but terribly flawed serial?
You get End of Time, that's what you get: an epic demonstration of just how spectacularly Logopolis could've failed.
Another of those moments where everything slots into place, and elements that provoked an under-the-radar "wtf?" reaction suddenly make sense. I think I get it: Rusty, looking for an appropriate way to finish off a massively popular Doctor's run, looks to Tom Baker's last serial for cues. And so we get an ordinarily-bubbly Doctor grimly brooding his way through the story, a mysterious but ultimately benign apparition acting as a harbinger of doom and handwaving the plot along, a self-indulgent sendoff sequence with prior companions, and a general ethos of "go big with the plot and the peril and the foreshadowing, even at the expense of explanations or making it all fit together coherently."
There are more similarities of course, but they mostly come down to the laws of statistics as to who the Big Bad will be: once Rusty settled on the Master, it made sense that there would be silly plots and counter-plots and both of them joining forces against a greater danger. That just goes with the territory; I don't think you can say he was drawing on Logopolis specifically, except perhaps in the decision to make the Master's character arc almost as important as the Doctor's. You could probably write interesting meta comparing those two Master plotlines, but I don't think Rusty was specifically ripping off Logopolis where the Master is concerned, more like implicitly working with it as prior, related canon.
The difference between Logopolis and End of Time, and the reason EoT crashes and burns so hard, is that Logopolis has a really neat idea driving it. Unravel all the techniques they use to amp up the dread and foreboding for Four's exit, dodge all the various plot holes, and you've still got entropy and recursion and a planet of spoken mathematics where the human brain can handle the sort of tangled recursive hierarchies that short out formal systems. Even here, the execution could've been more polished, but it's still one of the coolest and most original universe-imperilling threats the show has come up with: Arcadia meets Gödel, Escher, Bach. The techniques are all in service of something, and it's something the show has been exploring and will continue to explore in Castrovalva. Logopolis is flawed, but I'm willing to forgive its flaws (dodgy pacing, a few absolutely terrible sequences like the river idea, loose ends and plot holes galore in the final sequence, and the general impression that this is the second draft of what could've been an excellent script) for the sake of its central conceit.
End of Time has no central conceit, as far as I can tell. All the grim foreshadowing and grandiose language would've been acceptable to hype up a decent exit plot for Ten, but there's just nothing underneath them; they work to polish a slightly dented and misshapen gizmo like Logopolis, but you can't polish a turd. What the fuck is going on? What is driving this sequence of events? Shit just happens for no apparent reason, and Rusty waves his hands and mumbles about destiny and please pay no attention to that plot hole behind the curtain. And we are being asked to forgive all of this stuff for the sake of... what? It being David Tennant's last episode? Gimme something in the text. The closest EoT ever comes to a plot, and one of the only smart things Rusty did with it, is the reintroduction of the Time Lords as bugfuck insane and ready to blow up the universe to escape the Time War--there are about twenty minutes in there where I'm totally along for the ride, willing to forgive glaringly stupid things in the general vicinity of what's going on (o hai thar, Ten jumping through a skylight), and actually pretty fucking delighted that we get closure on the Time War. The only problem is that those twenty minutes have no connection to anything that's gone before, except for a bunch of people muttering that something is coming, so there's no way they can retroactively excuse the clusterfuck that preceded them. And they're ushered in with a staggeringly stupid bit of handwaving and a plot hole you could literally drive a planet through, neither of which build on anything in the past hour and a half. If you cleaned them up a little, they would make a great 45-minute episode, with all the rest of Rusty's personal pornography--the Doctor/Master fapping, the gratuitous SFX sequences, Ten's endless farewell tour--as DVD extras. But as-is, I'm not going to forgive any of the things that are terrible about EoT, because they are not terrible in service of a good idea, they're just trying to dazzle us into liking the awful bits. Desperate turd-polishing.
Basically it's a question of what you can get away with. Rusty took his cues from Logopolis and thought he could get away with a grand loosely-stitched-together plot and gratuitous foreshadowing and general hype for a popular Doctor's regeneration story. Right down to the companion flashbacks, which are silly and mildly self-indulgent for Four and ludicrously overblown for Ten. The only problem is that being Rusty, he dialed everything up to eleven, including the slapdash approach to the plot, and so ended up asking us to forgive a whole lot more on the basis of a whole lot less.