Not the same at all. The bat is the resonator in your example. Thats like saying you can hear the difference between a metal roof and a wood one. OF COURSE anyone could tell that. W/ your bat example, can you tell the difference in sound it made in the BALL? Thats what we're talking about.
Can you tell the difference in a musical drum hit only once w/ wood drumstick vs an aluminum one? Thats an example w/ better correlation.
That's a tough one. But I CAN tell the difference when wooden sticks have a different weight/pitch/resonance. Spent a lot of time over the decades picking sticks that were matched.