Here's kind of how I'd break down the Muppet/Muppety Christmas specials and films of years past to present. (Note I left out Sesame etc due to that being an almost separate issue for me.)
1.
John Denver & the Muppets: A Christmas Together
My memories of this special and the music contained are the reason it's my favorite.
2.
Muppet Family Christmas
It used to be down just a tad more on my list until my recent viewing of it in a room full of people. This special is best enjoyed with friends and family. There will never be another special like it.
3.
Emmet Otter's Jugband Christmas
This is such a beautiful world that Henson and company created for this special production. Pitch perfect in every way. I'd almost like to see a television series made out of it if done right.
4.
It's a Very Merry Muppet Christmas Movie/
A Muppet's Christmas: Letters to Santa
Tied for different reasons. The first was a bit too gloomy and snarky while the second was very musical but missed something by way of storytelling. I do enjoy both of these specials very much. If only you could stick both in a bag and shake them until the best parts mix together and rise to the top!
5.
Muppet Christmas Carol
A dark but handsome post-Jim production that continues to grow on me each year that goes by.
6.
The Christmas Toy
A forgotten special that came before Pixar's close facsimile. It's like Toy Story and the Velveteen Rabbit rolled into one television movie starring Dave Goelz as lead performer. A rare treat that deserved a better DVD release.
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I do think LTS has the Muppets heading in the right direction, however it does seem a bit bare-bones on some levels. Maybe that will help in rebuilding the franchise.