Well, it depends a bit on what you mean by performance. GPS speeds, upwind etc would probably be hard to measure a performance gain if you go for a lighter board, but if you're taking the feel when wave riding or ease of doing rotational freestyle tricks I think you will find a lighter board just feels nicer.
But it's good to have some perspective on it. Way back I was almost obsessed with light boards. But the last years I've ridden (wave) boards of all sorts of weights and some of my best ones have not been that light. But again, every time you step on lighter board you get a certain satisfactory feel from it.