Unless Doomsday's body could consistantly evolve past being effected by Asgardian magic,(which I don't believe it can) then I'm going to have to go with Odin on this one. I would even go as far as to say that Odin could soundly defeat Doomsday each and every time they fought. I mean damb..look at Odin's resume, he's taken on Ymir, Surter, Mangog, Mephisto, and a whole slew of others..each one of these peeps would own Doomsday..in my humble opinion. Odin has also bestowed power to people/things making them on par with the power of Doomsday(IE Beta Ray Bill, Destroyer, Thor, etc...etc)
Anyway..Odin wins....
i'm not too familiar with doomsday. all i know is that he's the first guy to acutally kill superman. and way i hear it, he comesback to life and evolves past the level of who or whatever beat him.
true, odin could kill doomsday. but he would just come back to life. of course, odin has so many ways to kill doomsday. but eventually, after the millionth time and a half that odin has killed doomsday, he would eventually evolve beyond everything and anything that odin could do to him and eventually win....theoreticly speaking of course. 😛
but like i said, this is all base on what i know of doomsday, coz all i was able to read was the death of superman 😛