Last Sunday the roles were reversed with Wallace and Gromit winning the Oscar for best animated feature.
Corpse Bride is set in 19th Century Europe, and tells of a man who is transported to the underworld to marry a mysterious stranger.
The eight-minute film Rabbit took best short and most cutting edge production.
It received the award ahead of Belleville Rendez-Vous and Wallace and Gromit: The Curse of the Were-Rabbit, which won an Oscar on Sunday for best animated feature.
The Gorillaz single Feel Good Inc won favourite music video in a category voted for by the public.
Rabbit - unconnected to the Wallace and Gromit production - was directed by the London-based animator Run Wrake.
Its storyline features a collection of old stickers found in a junk shop, which inspire a fairytale of lost innocence and greed.
Channel 4's animated series Bromwell High - set in a secondary school where the teachers and pupils are equally dysfunctional and voiced by a number of British comedians - was best comedy.
Best TV special was Angry Kid, which appears on BBC Three and is made by Aardman, the company behind Wallace and Gromit.
Honours were shared in the people's choice category for best film.
It was won jointly by City Paradise - telling of a young girl who falls into a swimming pool - and Who I Am And What I Want, about one man's life of excess.
Best music video
A commercial for the Observer Music Monthly magazine, which featured an A to Z of animated figures from the music industry, was voted top advert.
And the multi-genre American group Subtle collected the award for best music video for their track Swan Meat.
This is the tenth anniversary of the British Animation Awards, which recognise all forms of animation.
They were presented at a ceremony in London on Thursday evening.
ANIMATION AWARDS WINNERS
Best feature: Corpse Bride
Best short film: Rabbit
Most cutting edge film: Rabbit
Best comedy: Bromwell High
Best TV special: Angry Kid
Favourite music video: Gorillaz