It's Christmastime Again is a very strange special. It's one of the first culled from old strips (while Sparky was still alive, unlike recent ones which are pretty much obligated to) and elements of the episode were already animated in the Charlie Brown and Snoopy Show. But it has a strange feel to it that's almost like an episode of Seinfeld. I rather like this one, myself. Probably around as much as the original.
Looking at the more recent ones, Christmas Tales and I Want a Dog, I'd say Christmastime Again is better put together as far as straight up strip based specials go. Of course, Christmas Tales wasn't supposed to have a tie in plot and was pretty much made to fill up the hour that an uncut Charlie Brown Christmas left. I want a Dog isn't really a bad special, but the full hour runtime drags a bit. Plus it centered around a character Schulz didn't really like writing for anyway, and much like Christmastime Again, it reanimates strips already done by CB&SS, but changes the context so the plot sort of fits together (though it feels completely loose here). In the case of this one, the plotline about Spike coming over from Needles and Lucy fattening him up. In the original strips and show, this was done so he could fight the cat next door. Here, it's loosely connected to Rerun's story.
Now switching gears, if there's one thing I noticed more and more the older I got, it's the fact that the original Rudolph Rankin/Bass special was supposed to be sort of tongue in cheek. The problem is, it's so established as a classic, the subtle nods and satirical bends go over everyone's heads. What you really need to watch to get some context is the older Christmas cartoons made in the 30's and 40's (including the original original Rudolph cartoon which is usually on public domain collections). Those things are just dripping with sap, and the Rudolph special we know takes bites out of those old standbys. Think about it. The Elf wanting to be a dentist? Yukon's gold obsession and his general knowledge about Bumbles and how they bounce so they can shoehorn in a gooey ending where he becomes a good guy? All very much satirical bites at old sappy Santa cartoons. Heck, even Santa being kinda a jerk and his wife nagging him about being fat. And this is so much the establishment of cartoon Christmas specials, the satire wore off.