I give it to Nomad. I'm assuming his energy weapon would be unable to get through the neutronium outer hull of the Doomsday machine. But Nomad has a lot more thinking power than the DM, which is a pretty uncomplicated robot. No doubt Nomad would soon try shooting its weapon down the DM's "throat," and that would be that (frankly I always thought that it was way too easy to destroy the DM, but that's canon).
On the other hand, we don't know what the DM's anti-proton weapon, which can slice up planets, would do to Nomad, so one hit might be all it takes for the DM to take out Nomad.
Another possibility is that Nomad might be able to find an access port to the DM, and take control of it, maybe "merge" with it the same way the original Nomad merged with Tan-ru. But, IMO, the Doomsday machine, BECAUSE it's a Doomsday machine, was probably built without any access port.