it's still DS.. we dont say in forums he wins b/c he is big as a universe so he cant lose to superman... that is not how the character is written he is given a physical form to interact with the DCU for all intent and purposes that is DS when we are using him in comics or on the board.
who cares about whatever omega energy dimension he is in that his full consciousness physical body inhabits.
even then it doesnt even make sense either way if you look at DS origin story when he gained the omega power... he jumped into the dimension a few minutes or hours later he comes out brimming with power..
then you have him die repeatedly and finally in his last death some how he is connected to the Universe some how a trait that wasnt mention nor part of his character in his previous deaths or history?
that's like Odin one day dying and we find out that if he dies earth and all that is good dies with with him... BF'n Sh#$.
the PIS is that these New God's are considered abstract lvl tied to the DCU some how...