I have to admit that I'm not really a fan of any of them. I haven't seen
The Swan Princess since I was around nine, so that's out of the question, and so that brings me to Don Bluth. I honestly don't find really many of his films are that good (though I haven't seen
The Secret of NIMH), and his 90s stuff is a bit bland.
Anastasia is cringe-making as it basically takes true facts and turns it into little more than a fluffy little fairy tale. One could argue the same with something like
Pocahontas, another film based on a legend deriving from historical events, but that took place so long ago that any liberties are easily forgiveable, and it didn't really resort to heavy doses of the fantastic (aside from a talking tree and weird spiritualism involving leaves).
Anastasia, as much as it is supposed to be an adaptation of a legend, deals with historical issues from less than a century ago and that would have more directly affected current society (European communism only fell in the late 80s and early 90s), making it something one shouldn't really take that many liberties with. The opening that claimed everything was wonderful in Russia under the tsar was overthrown annoyed me (as awful as Stalin and co were, Imperial Russia was far from pleasant for most people), and using a curse from Rasputin as the catalyst for the revolution is just lame (again, with or without Rasputin around, those happy subjects were actually poor, starving and losing to the Germans in WWI). In short, the film basically whitewashes history to anybody with at least a tiny bit of intelligence or knowledge of modern history, and I find that rather offensive.
Thumbelina is reasonably charming in places, but most certainly below average. I can imagine Don Bluth said "right, so Disney beat our talking dog movie at the box office with a Hans Christian Andersen fairy tale about a girl who finds Prince Charming against all odds, let's take our shot at similar material to threaten them!", not really thinking things through. The film feels so lethargic in the same way that a number of Disney's late-70s/early-80s product does, as though everyone got really lazy not too far into the film's production and couldn't care less with certain parts. The film certainly had potential, but it ends up just resorting to cutesy numbers, and squeaky-voiced characters as though it's supposed to be a parody of a Disney film; honestly, it felt like the opening of
Enchanted without any of the irony and without much of the wit (did I mention that the script has thousands of plot holes, as though it were written by a grade-school kid?). The animation could have been better, and the character design in particular is lacking; I'm with Amy in disliking the animals' designs and honestly don't think many of them look like the animals they're supposed to (don't get me started on how the farm animals all wear hats, including chicks just popping out of their eggs). Some of the songs are bad/annoying (especially the ones the frogs and the insects sing), but one or two stand out as nice enough ("Let Me Be Your Wings" has a nice enough melody, and I thought that "Marry the Mole" was harmless).
I have to say that, with a lot of the non-Disney animated films of the 90s, there seems to have been a conscientious effort made by executives to try and emulate the Disney formula, at least in the latter half of the decade, with films that ultimately seem overly micro-managed and messy. The best non-Disney traditionally animated film of the 90s I've seen were probably
The Iron Giant and
The Prince of Egypt. The former was a film that took some risks and ended up working pretty well (good old Brad Bird

), and the latter was tasteful and entertaining despite following the Disney pattern.