Pre-Upgrade Kurse loses, while post-upgrade Kurse wins. Same can be said vise varsa for Doomsday.
Kurse might be strong enough to tussle with Doomsday and break him... I don't know if he could keep doing that though since Doomsday can adapt and come back.
Depends on which version of Doomsday, and Kurse.
Kurse is one of the guys i find very hard to argue on.
He has been said to be 4 times stronger than Thor, which i suppose is pretty cool, the problem being he really, really lacks high end feats (i am missing about 17 appearances of Kurse, so i would be surprised if he has done anything drastic in those 17 appearances but if he has apologies).
From what i have seen Kurse has been stated to pak massive, massive power, but lack feats.
I mean, he punched Superman into essentially death m(the shock wave was powerful enough to shatter all the windows in the city, but somehow no one in the area went deaf, which is just weird) , but Kurse was able to survive the combined power of Stormbreaker and Mjolnir (like, all of there reserves funneled through that one blast, the hammers had to be recharged after that) which is pretty extreme (I doin't know if that would be on level with surviving an Omega Beam, (what are the highest feast those have? injuring Superman?) anyways, I think Kurse could at least manage a draw in most scenarios ( he was able to fight Thor and BRB fairly easily)