These are anthologies that I considered "major" in the sense that there was a lot of buzz about them. Most of these came from big name publishers, though these days the definition of "big name publisher" is iffy. With one exception, these were published as hardcovers or trade paperbacks. Now, certainly some of the anthologies I've put in other categories easily qualify as "major" -- for instance, The Beastly Bride or Legends of Australian Fantasy. Many (most?) other anthologies were published in at least trade paperback. Some were published by "big name publishers". So partly it's that these books don't readily fit somewhere else! (Finally, when I say "major" I don't mean "better", just more prominent.)
Here are the six I put in this category;
Shine, edited by Jetse de Vries;
Warriors, edited by George R. R. Martin and Gardner Dozois;
Swords and Dark Magic, edited by Jonathan Strahan and Lou Anders;
Gateways, edited by Elizabeth Anne Hull;
Stories, edited by Neil Gaiman and Al Sarrantonio; and
Songs of Love and Death, edited by George R. R. Martin and Gardner Dozois.
Notably, two of these are explicitly mixed-genre -- Warriors and Stories each contain SF, Fantasy, Horror, Historical Fiction, and Mainstream. (In those cases, I've categorized a few non-fantastical stories as "Fantasy" for my counting purposes, though I should note that only a very few are really straight "mainstream" -- even some that are close have slight or slant fantastical elements (such as Roddy Doyle's "Blood", from Stories, which is about a sort of vampire, even though it's not really fantastical).)
Between the six books there were 113 stories for a total of a bit over a million words of fiction. Two of the stories were reprints. The new stories included 5 novellas, 54 novelettes, and 52 short stories (3 short-shorts). 47 of the stories were SF (42%), and 36.5 of the authors were women (33%).
My favorite novella was Elizabeth Hand's "The Maiden Flight of McCauley's Bellerophon" (Stories), and I also greatly liked George R. R. Martin's "The Mystery Knight" (Warriors) and Cory Doctorow's "Chicken Little" (Gateways). Strong novelettes included Neil Gaiman's "The Truth is a Cave in the Black Mountains" (Stories), Gord Sellars's "Sarging Rasmussen, a Report (by Organic)" (Shine), Alastair Reynolds's "At Budokan" (Shine), and Howard Waldrop's "Ninieslando" (Warriors). The best of the short stories were "Bloodsport", by Gene Wolfe (Swords and Dark Magic); "The Thing About Cassandra", by Neil Gaimain (Songs of Love and Death); "A Suitable Present for a Sorcerous Puppet", by Garth Nix (Swords and Dark Magic); and "The Cult of the Nose", by Al Sarrantonio (Stories). Other strong work came from Gardner Dozois, Michael Moorcock, Joe Haldeman, Wolfe again, Cecelia Holland, K. J. Parker, Joe Abercrombie, Tanith Lee, Scott Lynch, Peter S. Beagle, Roddy Doyle, Vernor Vinge, Carrie Vaughn, and Robin Hobb.