Zod has the same potential as Superman, but less time to adjust to Earth. Since full power Superman ended in a mutual kill(-ish state), Doomsday would probably win.
That kinda reasoning has always been flawed, as there are other factors to take into account. It’s sometimes called the coat fallacy: I fit in my coat, my coat fits in my bag, therefore, I fit in my bag.
As far as I know: Zod is a General with the same potential as Superman while Superman is a... reporter. Given the same time to adjust to Earth as Superman I would go with Zod. By logic, he should be a much better warrior than Superman, although Doomsday is a whole different kind of monster due his to his evolution thing. With some preparation, General Zod should be able to take out Doomsday