There is usually no meaningful advantage to taking an earlier slot purely because it is earlier. If the original date was confirmed and still works for the firm, you should choose the timing that gives you the best chance to perform well.
That does not mean you automatically need the extra week. If you are already ready and the earlier date is more convenient, taking it is perfectly reasonable. But do not compress your preparation because you think interviewers will reward you for being first.
The one exception is when recruiting explicitly tells you that timing matters because roles are filling quickly. In that case, the tradeoff becomes more real and you should ask for clarity.
Otherwise, optimize for performance and logistics, not for perceived signaling.