Quoted from CrazyLevi:You guys certainly have better memories than I do...I can't say I ever noticed that the original pac-man I played 40 years ago had a leaf stick, or that I noticed the difference on newer versions with a microswitch.
Is there a reason you guys prefer the leaf switch beyond the nostalgia of it not making clicking noises? Seems like a micro has better feedback/accuracy.
I'm not an arcade purist or guru, but have noticed and come to appreciate the difference between clicker and leaf swtiches, and prefer leafs *when available*.
In one way you're correct in that there is no logical difference: input is input. Close the switch, move Up (up down down left right left... oops) 
Assuming the travel is identical, the end result of clicker vs leaf is the same.
But a clicker has an active detent that resists movement until you supply enough force. Minimal though it may be, that feeling is there. And then it "snaps back" the same way. Whereas a leaf just bends and yields smoothly, fluidly. There's resistance but nothing harsh.
By design and definition, this mechanical distinction cannot be overcome, and for some people the difference is purely subjective. So, since I know you hate carguments let's forge an analogy from the audiophile realm: With regard to tactile feedback clickers are a digitally "jagged" waveform, and leafs are analog "smooth" ones. Is it more pleasant to slide down stairs, or a smooth ramp?
Play Pacman with a clicker and then with a leaf and I guarantee you'd prefer the leaf. It's smoother and just feels more pleasant to play. Some folks might say it's faster.
Personally for me, a clicker isn't necessarily a deal breaker - I'm not that good, I can still play the game. A cheap clicker might be enough to scratch the itch. Some games you might not even notice. But given the choice or opportunity to upgrade, a leaf is the way to go.
