Wing design is a fascinating thing, but twisty as well.
While a bigger wing generally creates more drag, it also generates more lift, so its a two sided coin.
Wing width is also important, for a wider wing comes with worse aspect ratio, so in order to say how a bigger wing performs, the answer depends slightly whether it is longer with the same basic shape, or wider. A bigger wing does thereby not nececcarily have to have worse aspect ratio if the wing is just made bigger by increasing the span.
Typical planes to compare in this sector are the Spitfire and the 109, - while not the same plane, they are in many ways similar. Similar in weight, size and power output, the wing sizes and shapes are totally different. The Spitfire has a wide wing, sacrifizing the aspect ratio to some 10% worse than the 109 (if my memory serves me right), but for almost 50% more wing area.
The 109 has more acceleration, while the Spitfire holds better in turns, so between those two, the bigger wing and worse aspect ratio of the Spitfire still more than balances it with its higher lift.
As the Spits were chopped and cropped for better rollrates, they also became faster, but worse at turnfights.
Very many sides of this indeed:)