This is one of the weirder matchups, as Chewbacca is one of the wild cards.   

Chewbacca vs. Doomsday

Origin:

A Wookie general on his home planet of Kashyyk.  When the republic fell he ventured into space as a smuggler but soon joined the rebellion. 

Doomsday was created by a mad scientist named Bertron on the planet Krypton. It was an organism that was built to seek perfection through battles (like Pokemon) and was thus constantly evolving. Since its inception, Doomsday has left destruction and glares of doom to wherever he travels in the galaxy.

R: Chewie's origin is good, but Doomsday's is better.

U: Doomsday – His origin is just about the only good thing about him. It speaks of a science gone wrong, a horrifying alien entity, and destruction. The origin makes the characters whereas his later stories only do harm to his character through inconsistent portrayals.

Powers:

Strong, but not to a supernatural level.  Also presumably pretty insulated against the cold. 

Doomsday has super strength at the level of Superman. Plus he has accelerated healing at the level of Wolverine and he is technically immortal because whenever he dies he comes back with immunity and can never be killed twice in the same manner.

R: I am not sure if getting hit by the Millenium Falcon traveling past light speed would even stop Doomsday 

U: Has Doomsday ever been killed by a gunshot? Oh well not like it matters, this will end in one blow.

Costume:

Well its not a costume per se, but the bandolier for his bowcaster is pretty iconic over his heavy fur. 

He doesn’t really have a costume. But he wears shorts like the Hulk!

R: I agree, but the bandolier is so iconic.  You could show that to a lot of people and they would recognize it, so I go with Chewie here.  

U: Tie – Neither of them has a costume and both look like animals.

Personality:

Loyal and trustworthy friend and noble warrior. 

It’s only in fairly recent stories that Doomsday has begun developing something of a personality and intellect. For the most part if it exists it’s suppressed amongst his numerous rampages.

R: Chewie is one of the best characters in all of Star Wars (and there are lots of good ones) 

U: Doomsday developing a personality through his evolution process just doesn’t feel like a good fit and even seems self-defeating to previous stories. Chewbacca’s personality however, is what makes him an interesting character.

Aesthetics:

In terms of aliens in the Star Wars universe, Chewbacca is one of the least weird looking ones but also one of the most beloved. 

Doomsday is a massive monster. The color of his skin is grey possibly for he should have decayed by now if not for his healing factor.

R: I wouldn't pat Chewie, but I would love one of those Chewie hugs that he gives his best friends.   

U: Tie – Both of them look like monsters so I’m not going to pat either of them.

Best Story:

Can I just say the comic book adpatations of the Star wars movies?

His first coming to Earth which also resulted in the Death of Superman. Although the changes didn’t stick, every other Doomsday story after it seems to fall short in light of that one.

R: I will go with a tie, Chewie is not that pivotal in the movies, and Doomsday's first appearance sort of changed modern DC.

U: Neither of them has a laundry list of stories but I would say Chewbacca solely for the movies.

Fun Fact:

Was designed after George Lucas's dog. 

The death and killing of Superman by Doomsday resulted in four new Supermen – Steel, Superboy, Eradicator, and Cyborg Superman.

R: Two of those Supermans turned evil though.  I will go with Chewie here, but would be interesting to see a Star Wars character based off of Superman's dog. 

U: And Doomsday was designed after Ryan Reynolds when he looked into the mirror. Never mind that! It’s probably cool to be designed from a dog. *whistles*

Media Appearance:

Star Wars episodes 3-6, numerous animated versions of the show, and even the Star Wars Christmas Special! 

Doomsday appeared in Justice League Unlimited as well as the movie Superman: Doomsday

R:  Let the wookie win! 

U: Chewbacca won an MTV award for his work. Has Doomsday done that?

Whereabouts:

Is apparently dead, which is not very good, but comics are not the highest level of Star Wars canon and can always be overwritten by Lucas. 

Currently going toe to toe with Superman in Action Comics in the story called the “Reign of Doomsday”

R: I will go with Doomsday here, although Chewie does get to hang out with Jean Grey and Batman's parents. 

U: ‘Tis better in comics to be dead, than be in a mediocre bad story.

Chewbacca: 6 + 5

Doomsday: 2 + 2