You should follow that smilie's path.
Superboy Prime will not beat this version of Doomsday.
Do you want me to explain why?
The way Doomsday was written in H/P he could evolve immunity to the means used to previously kill him. That is how he managed to evolve from being a normal baby into the ultimate killing machine. The fact is made more relevant when Doomsday encounters the radiant. The radiant is an energy being that managed to beat Doomsday once. Needless to say, and with Cyborg Supes' help, Doomsday has a 2nd round with Radiant and guess what? Doomsday one shot Radiant. Even the waverider knew Supes would die if he was to face H/P Doomsday since Kal-El would not be able to kill Doomsday in the same manner he did before. That is why Superman got motherbox to amp himself. He needed it just to hang with this new version of Doomsday.
Do note I am not even bothering to bring to the table that Doomsday evolved after getting oneshot by Darkseid's Omega Beam.
In the end with all the enhancements by motherbox Superman could not tackle Doomsday. The only way they could destroy this version of Doomsday was to teleport and Entropy his ass for the win.
There is no way, I repeat, no way Superboy Prime will be able to duplicate that feat. So while it's true that Superboy Prime will hang with Doomsday for a while it is impossible for SBP to beat Doomsday because physical force won't cut it and when all is said and done that is all Superboy Prime has going for him.