Logic and reason rule the pages of Hard Fantasy and attention to detail is a writer's best gift. Hard Fantasy is the Fantasy version of Hard Science Fiction, but the two aren't completely analogous—Hard Fantasy is not just Fantasy that treats magic like science. Fantasy is 'hard,' when it is concerned with how and why things work.
Hard Fantasy also does not pull away from the traditions of the genre, as Mundane Fantasy does, but instead offers a detailed explanation for the existence of magic itself, magical creatures, and seemingly fantastical settings. For example, dragons with an evolutionary past, rather than legendary. Hard Fantasy takes fantasy's traditions and the mundane details and uses them to create a complex and meaningful story—an enchanted sword is not taken for granted, it has ramifications within the story the justify the detail needed to explain how and why it has been enchanted.
High. Magic in Hard Fantasy probably isn't going to seem as wondrous and fantastical as other Fantasy stories, but magic will be detailed. Magic will be understood by the reader and the characters in the story—it is a system with rules. This does not mean that magic is scientific, because the rules that govern magical systems may not be logical principles, but there is an internal consistency.
Moderate. Because world-building is taken very seriously in this sub-genre and because the resulting world, while imaginary, has a strong sense of realness, a commentary is offered on our world by inevitable comparison.
Moderate. Because world-building is so paramount in Hard Fantasy, character building can become a bit lax. This is done (in part) to help balance the overall story; because there is so much detail in world-building, to put the same level of detail into characters would result in a very heavy story. Thus, Hard Fantasies that have well developed characters also tend to be quite slow moving.
Moderate. Plot development is a fine line to walk in Hard Fantasy—it has to balance all the details of world-building, while keeping the story moving forward. So yes, sometimes the plot can seem to stall a bit while readers learn how dragons came to be in the world, but eventually it will be beneficial to the overall understanding of the story.
Variable. Hard Fantasy is often linked with the gritter, darker sub-genres of more modern fantasy that incorporate high levels of violence. But, it can just as easily be linked with the brighter and more optimistic sub-genres.
Mundane Fantasy. Mundane Fantasy strips away all the cliches, Hard Fantasy makes sense of them. You're not going to find cliched elves and wizards in either sub-genre—both will present them differently, but they will be fresh.
Epic Fantasy. Hard and Epic Fantasy both develop rich and complex worlds and spend plenty of time on details (languages, races, social structures, histories, magic systems).
Most other sub-genres. Hard Fantasy is an approach to world-building and it is a skill that can be incorporated into most sub-genres.
By Robert A. Heinlein. Magic is a common skill used in various fields and businesses, so naturally there is a whole magical bureaucracy to contend with.
By Poul Anderson. This classic Fantasy novel uses traditional Fantasy tropes and makes them new, it also introduces the multi-verse and uses quantum mechanics to travel between worlds. The story also draws from Arthurian legend and Norse mythology.
By Larry Niven. Originally published as just one novella and then later turned into a collection, these stories ask the question, "What if magic were a finite resource?"
By George R.R. Martin. This series is known for its grit, but it also is a great example of the detailed world-building characteristic of Hard Fantasy—the world's geography, its history, its politics, its religions, are all carefully crafted with a great degree of internal logic.
By J.R.R. Tolkien. The Lord of the Rings. Tolkien is unbelievably detailed in his world-building, he crafts entire languages, massive family trees, and eons of history to make up his Middle Earth. So while there is a definite sense of 'hard' to LOTR, some things do remain a bit soft, but that's okay.
By Patrick James Rothfuss. A world that is vast, fantastical, and strongly rooted in logical world-building—it is a trilogy and biography of a famous musician and adventurer.
By Laurence Yep. The third book in a tetralogy, is about restoring the lost home of dragons. The hero of this story uses reason to solve a magical problem—trapped on a magical island.
By Brandon Sanderson. This series has a complex magic system, history, and religion, and all of these things are interwoven to create a rich world in which the dark lord rules.
By Naomi Novik. This alternate history tale is about the Napoleonic Wars, but dragons are used in aerial warfare.
By Robert Jordan. An epic series that is known for its detailed and imaginary world—not to mention a well developed magic system. Jordan developed an entire mythology that attributes the creation of the universe to a deity, not to mention cultures, histories, magical powers, and struggles between good and evil.
By Lyndon Hardy. A series with the most logical and detailed magic systems ever invented. This is one for those analytical readers who like magic to actually make sense and follow consistent rules.