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The handling in GT3 is far better than 2, since the developers spent more time getting the real car physics just right in the game. All the cars handle differently to one another.
Plus the graphics in GT3 are amazing, they really show off the power of the PS2. All in all, I think GT3 is the best of the series yet.
With GT3, the championships are organised better, and there are far less car specific championships.
With this in mind, and the graphical supremacy, and handling tweaks, GT3 is my favourite.