Ancient DNA is pretty degraded, so it's hard to get an exact number. It's estimated they diverged more than 5 million years ago, so it's probably hundreds or thousands of different genes.
Scientists rewrote 14 key genes in gray wolf EPC cells to express 20 dire wolf traits meaning that "no ancient dire wolf DNA was actually spliced into the gray wolf's genome."
They separated pretty far back, so they're about equally related to jackals, dogs, wild dogs, various wolf species, and coyotes.