I have noted that different balls sound different and feel different.
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[*] Sound tends to range from soft "thuds" in more expensive short-game oriented balls, to sharp "tings" in cheaper/harder distance-oriented balls.
[*] Feel tends to range from softer more seemless impact in the more expensive short-game oriented balls to harder more punched impact in the distance-oriented balls.
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But I have not noticed any actual difference in performance. I have taken several balls of various types out with me onto putting greens and practiced putting, and I have yet to be able to determine a difference in actual performance. If there is one, I'm not good enough to, side-by-side, tell a difference. If someone were a terrific putter and could control their putts down to the inch consistently, I wouldn't be surprised if one ball traveled an inch farther than another or had 5% less skidding, but I would expect that to only be a very minor deviation in performance, only relevant for a really good player, and probably only noticeable between the extremes of ball types.
Part of the problem is that, psychologically, we get primed by our senses to expect some things. When we see and feel a certain kind of impact, we're mentally prepared and probably biased toward observing it. I've heard people say that certain balls seem to go farther/shorter, or roll differently. But people also mess up their assessment of every other type of shot in golf, so I consider such hearsay untrustworthy. :-)
I would be open to hearing from a good putter who has conducted extensive side-by-side tests between several ball types and performed some sort of measurements (even if they're just relative to each other). It may not be perfect, but it'd be interesting to hear, and certainly worth more than people comparing balls across different rounds on different days.