Adamantium is the stronger metal . It's been said that wonder woman could snap deathstrokes Promethium staff. Whereas no one has broken Grade A adamantium yet.
Depends on if it was before he got that staff or not. His equipment got upgraded all the time in the issues, at first he had a stuttering boy making all kinds of tech for him, then later in the series, the governement took all his gear and modified it to top quality. At first the staff and sword were made out of 'italian metal'.
Deathstroke's staff, sword and chain mail have all been broken (or disintegrated) several times. The either aren't made of Promethium or Promethium isn't has strong as adamantium
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I don't know much about DC promethium , I do know that the real life Promethium has a tensile strength of 70 MPa(ranked 19th) , and along with all its isotopes , is radioactive .
So , I'll pick adamantium .
The adamantium that Ultron was composed of when the Hulk dented him was confirmed as being secondary adamantium, a less expensive but less durable form of adamantium. The adamantium in Wolverine's skeleton is true adamantium, the second most durable form of adamantium. It is completely indestructible except to potent cosmic, magical, etc. entities and someone with excellent powers of molecular manipulation. It has been theorized that true adamantium of greater mass, sharpened, delivered with great force, and superheated could also damage true adamantium. The adamantium in Captain America's shield is called proto-adamantium, and is the most indestructible substance on Earth. It is also impossible to recreate since it was made completely by accident. Thor was able to dent Captain America's shield with the full power of Mjolnir when he had the Odinforce. Beyond that, in 616 Cap's shield has only been destroyed by two individuals: Thanos with the Infinity Gauntlet and the Serpent, the Asgardian God of Fear and Odin's brother. After the latter, Cap's shield was reforged using the shattered pieces and Uru, which for those that don't know is the metal that Thor's hammer is made of.