One comparison between du Maurier's short story and the Hitchcock film is the sheer terror that the birds pose, while a difference might lie in characterization.
I think that a significant difference between both works lies in the main characters. In du Maurier's short story, Nat is the central focus. He is the lens through which all of the action takes place. We tend to see the horror of the ornithological attack through his eyes. Hitchcock's film takes a different tact, as Melanie Daniels is the central focus. Mitch occupies importance, but is secondary to Melanie. While du Maurier focuses on Nat, his demeanor, and his heroism in the face of overwhelming odds, Hitchcock focuses on how Melanie perceives everything around her. Melanie is attune to the emotional, psychological, and physical condition around her. For example, Hitchcock pays special attention to how Mitch's mother is at first apprehensive towards Melanie and then nurtures her. Melanie also recognizes the nuances between Mitch and Annie. This level of characterization is not present in the short story, where the threat of the birds and its impact on all of humanity is more dominant.
Both works communicate the fear of the birds' swarming attack on the humans. du Maurier illuminates the powerlessness of human beings in the face of such a reality. Nat is left to regret the fact that everyone around him is dead. When he sees no smoke coming from his neighbor's chimney, the terror of the birds is evident. The world that du Maurier creates is apocalyptic, one where the birds have wiped out the humans. This same feeling is communicated in Hitchcock's movie. The birds' eye view of the chaos in Bodega Bay is one such instance. The birds' massing on cue as the townspeople are incapable of dealing with what is besieged upon them conveys a sheet sense of horror. The final scene where Mitch's family and Melanie leave as the birds are victorious communicates the same bleak vision offered in du Maurier's work.