Would you say the PS2 had better first party support than the GameCube?

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PS2's first party lineup was pretty average honestly. It had some good games, but nothing on the same level as say Metroid Prime.

On the other hand, Gamecube had the weakest first party lineup of Nintendo's home consoles due to games like Sunshine, Wind Waker, Jungle Beat, Double Dash, and Starfox Adventures going in weird directions that made them worse than their predecessors.

So both are underwhelming to be honest.