Neither, because all Pagan gods and goddesses (Poseidon and Hades included) are immortal. Unable to be killed. They can however, be trapped, as Ares was in a Jar, or be intimidated, as Zeus does regularly to the other gods. So long as the battle is physical, this invulnerability holds true.
If it were a battle to submission... that's up for debate.
Poseidon because hades has fire powers but Poseidon has water powers and water could vaporise fire.
The big three of the Olympians were Zeus, Poseidon and Hades. Zeus was recognized as the champion as he was the only one willing to face Typhoon. However they are all three a close match and whenever they have come close to 'coming to blows' they have always chosen a mediator to settle their disputes.
Zeus and Poseidon quarreled over Thetis a nymph and instead of fighting over her they submitted to the mediation of Prometheus, who gave Thetis to King Pelus.
Hades kidnapped Persephone the daughter of Ceres. Ceres appealed to Zeus to rescue the girl but Zeus was disinclined to get involved. Ceres then caused permanent winter to come over the Earth so Zeus worked out a deal with Hades where Persephone spent half the year above ground, the other half below.
Unlike Disney believes, Hades is not evil. He is more like a gatekeeper.
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