Comparatively speaking? Wonder Woman was capable of contending with DOS Doomsday for a time on a physical level. Which tells me that a regular Thor could also contend with him for a time as well. The only glaring difference that sticks out to me is; Thor with the hammer happens to be drastically more powerful than she is. At least in terms of power output, and physical striking damage. While she is drastically faster than he is. Thor with the belt and going in for the kill, may in fact just be able to knock DD's head clean off.
Here's why.
Thor knows what Doomsday is going in to the battle. Backed by forum regulations.
Thor has affected more powerful guys than DOS Doomsday. If we looked at the force that it took to put DOSDD into a coma, Thor would absolutely demolish this guy with feats (Rage, Celey, or anyone invested may have to jump in with the scans. I have none sorry). The force that it took to put DOS Doomsday into a deep coma shook the city, and blew out windows for over 10 miles of the impact. Thor can blow up planets with his attacks. Waiving this fact after arguing power levels on a regular basis, would IMO be a double standard. Belt of strength Thor in my unbiased opinion is overkill due to what I mentioned above concerning DOS Doomday's ability to weather an attack from Thor. The only way that I can possibly see Thor losing this, is if he held back drastically, while attempting to reason with a guy that he knows coming into this match could not be reasoned with. Let's just scratch that idea, it would be completely out of character.
BOS Thor FTW.