White has more initiative, while black is more passive. In a sense, white can be one step faster than black, and black just keeps up
Which color are you better with?

I have a higher winning percentage with White, but pretty well all of my spectacular "big wins" have been with Black.

White moves first (there's an advantage for white for moving first), so white can develop fast and attack the black, whereas, black mostly would have to play a defensive game. White has a slight advantage because of this. There are many aggressive gambits for black though.
Read about The first move advantage for white here
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most people say white, but i often find (atleast notice) myself playing better when i play black