"The Dying Earth" is not a novel. Even its parts are not novels, but a collection of short stories. First part, "Mazirian the Magician", is just a collection of short stories, with stories connected only barely with setting and some characters. The second two parts, "Cugel the Clever" and "The Skybreak Spatterlight", are novels (actually, fix-ups) telling stories of travels of Cugel, who travels the world trying to get home and exact revenge against a magician who sent him away. And the last part, called "Rhialto the Marvellous", is composed of three longer stories with common characters. Just to clear it up, these are mostly comic stories.
First, "The Dying Earth" is different from anything I have read so far. Maybe "Discworld" stories by Terry Pratchett are the closest thing to it. The world is full of magic, maybe even too full. It reminded me on old Conan stories. There is literally magic on every step: spells, creatures, objects... Vance doesn't even care to try to be realistic The "plots" takes place on Earth, but long in future, when the Sun is closing to its death and magic is again present on the world.
The style of the stories if definitely vintage, not something you would mistake for a modern fantasy. A bit pompous, you could say. Many concepts here looked familiar to me - and I realized that many modern fantasy writers copied Vance's ideas. I was there Chine Miéville got his idea for "The City & The City", and some other ideas used by new authors. If Vance patented his stories, every fantasy writer would have to pay him royals for using his book.
Since these are stories, you don't get to know the characters too much. This changes a bit in Cugel's stories, where we spend much time with him. But when Vance decides to focus on a character, he can do wonders (e.g. Drofo the worminger-sage). I found it unusual at first how everybody just keeps running all around the world; nobody stops to make any strategy. Women are mostly either victims or evil, or sometimes innocents in need of male guidance.
As of my impression. First part consists of six stories loosely connected. I can't say I really liked them, but they were OK and sometimes funny. Two Cugel novels were much, much better. They had a structure, a regular main character, an ultimate goal. And they were very funny! They are a bit long, but I didn't mind it at all. On the other hand, Rhialto's stories are not quite as good. Vance is obviously trying too much where he was effortless before, and I wasn't able to enjoy them. And even though you can't say that this book was planned to be consistent, these last three stories were even more inconsistent with previous...
But all in all, I had more good times than bad with this omnibus. "The Dying Earth" is definitely something that any real fantasy-fan needs to read, at least just to know where many of ideas came from. Maybe not a book to buy, but definitely a book to read.