Eventually DD would be able to beat Drax, but no in the beginning. DD does not instantly recover from death more powerful. It takes time. Which means that Drax would at least beat him the first time, "as is".
Drax has high-level cosmic powers. He gets power from the universe itself. There is no limit.
DD powers are still derived from a biological point. He has to evolve his method of defeating Drax. But, eventually, he probably could.
i havent seen powers very impressive from drax he cant even beat thanos, and he gets bossed around by Warlock DD would kick his butt, DD did defeat a motherbox powered superman and waverider and a darkseid avatar
Also, Doomsday has near instantly recovered from Death.
In Hunter Prey the Darkseid Avatar Omega Beamed him.
He was dead, then popped back up.
THe Darkseid Avatar said something very close to [I don't feel like actually grabbing it, lol just got off work dont feel like digging through comics.] "So it is true, you have evolved beyond death."
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I am God's mighty fist. I am God's strength made manifest.
Sig by: Skeets, S.S, thesilverspider, Sir SKEETS Alot
Drax ripped the core out of a star (which is much more impressive than any strength feat shown by Doomsday), and also ripped Thanos's heart out. Both of those feats were accomplished without the Power Gem, with the gem Doomsday is outclassed. Besides Drax can recover from death as well, and the OP only stated that Doomsday gets two "lives".
Some say that Drax being Thanos kryptonite is the reason why he was able to rip heart out (not by pure force). Although Ripping the core of a star out is an ok feat, it is still only 1 feat. Also, the problem is that it is more of an energy causation feat instead of a pure strength feat. It takes energy powers to grab something that can not be grabbed (as a whole). It is like me grabbing the entire beach by grabbing on to some sand. Even so, I wouldn't rank it higher than say holding black holes, moving planets against the force of beings who possess many stars worth of power, lifting infinite weight, or resisting the OE at point blank range. Superman did all of those feats except the last one.
HP DD has proven to be stronger than current Superman. He prove it in OWAW. Anyone stronger than Current Superman is stronger than Drax with PG (by feats of course). Drax with PG is probably slightly more powerful than without the PG since he was too dumb to access it's potential.
With that said, strength doesn't matter here since DD's durability will hold up to Drax long enough to both heal (assuming Drax can even damage him) and to adapt on the fly to be even more resistant.
Plus DD is far faster and more relentless. I see DD tearing Drax up in a matter of moments to be honest.
Does that make sense to you?
Doomsday from the Hunter Prey saga in 1994 proved he was stronger than current Superman because a later saga Doomsday did something in 2001?
You're implying that just because Superman can do something than Superman can as well. Just because he can kick Superman's ass in a fight doesn't mean that he is capable of the same strength feats. It's possible that Dr. Zoom or Flash could also beat Superman in a fight. That doesn't mean that they are the same in strength. Give me one example of Doomsday doing something that would rival Superman in strength, other than just kicking his ass. Drax could be Thanos's kryptonite, but the same argument could be used for Doomsday and Superman.