For the majority of golfers whose swings aren't close to ideal, not much. For good golfers with reasonably consistent swings, who make good contact with the ball, the more expensive balls offer more precise control of ther shot. Many balls can offer “ distance", but more expensive balls can offer, in addition to distance, lower or higher trajectories, more spin control on approach shots or chip shots around the green, a better “feel" off the putter- or the desired combination of all of the above. They allow you to fine-tune your game.
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I prefer to be aware of all the aspects before making any purchase. I am a big fan and fond of this game greatly