As a removal spell, Ceaseless Hunger is the clear winner; hits two targets instead of one, for one less mana, and exiles instead of destroys them.
As a permanent, Infinite Gyre is the winner, though the race is closer than comparing them as a removal spell; a single attack by either is usually not a game-ending threat, but letting either live for very long can end up a serious issue. Gyre becomes a problem much more quickly than Ceaseless Hunger, though.
As a card in the library, Ceaseless Hunger does absolutely nothing while Infinite Gyre can protect you from mill and can be involved in some combos (for example, Syr Konrad, the Grim+Basalt Monolith+Mesmeric Orb).
As a permanent, Infinite Gyre is the winner, though the race is closer than comparing them as a removal spell; a single attack by either is usually not a game-ending threat, but letting either live for very long can end up a serious issue. Gyre becomes a problem much more quickly than Ceaseless Hunger, though.
As a card in the library, Ceaseless Hunger does absolutely nothing while Infinite Gyre can protect you from mill and can be involved in some combos (for example, Syr Konrad, the Grim+Basalt Monolith+Mesmeric Orb).
Two Score, Minus Two or: A Stargate Tail
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