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It depends on what style you play, in my opinion. If you do fingerstyle or classical, you don't even need a pick, but if you play rock or metal it makes quite a difference: a thick, rigid one gives you a dry, defined sound, a thin one is softer and more flexible. It's not like it'll completely change your playing, but once you find the right one for your style you realize it's not just habit - it's like using the right sticks when you're playing drums.
It really depends on what you're playing and how. With a classic pick you get a more defined and precise attack, especially if you're doing fast rhythms or lead work; without a pick or using your fingers you get a softer, more natural sound, perfect for fingerpicking or more delicate styles. It's not that one is right and the other wrong - it's that they really do change the tone and the feeling you're conveying. A lot of musicians switch picks depending on the song, so in the end it's important to choose the right tool for what you're trying to achieve in that moment.
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