Freaky Friday notion

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What would happen if Jeeves and Alfred Pennyworth (Batman's butler/valet) were swapped by handwavey fiction magic?  How would they all react to each other?  I think Alfred would be very kind to Bertie, although a bit too indulgent maybe in sartorial matters.  Jeeves could be invaluable to Bruce Wayne, but I'm not sure he'd ever see eye-to-eye with him on going out in public in a rubber suit.