If this is a question that you are unsure about, then a quick Internet search will provide all of the answers that you could possibly need. Unfortunately they will all be different! Here are a few answers, taken from the actual Internet...
These are interesting answers that point out how complex this issue is. The fulll answer won't be achieved in a few words. This question warrants a detailed examination.
I should point out that my comments here are directed mainly at the steel-strung acoustic guitar, where the difference between new and used strings makes more of a difference, but it is relevant to all kinds of string instruments. Here goes...
There is a difference between strings that have been used, maybe well-used, and strings that are old. 'Old' I would take to mean strings that have passed their point of usefulness. They have been used and used again until they sound bad and their only practical application would be if you actually wanted a bad sound. This isn't an impossible scenario, but I intend to concentrate on sounds that are good in various ways. Strings that are old might be out of tune along their length, might have patches of corrosion that scratch against the frets, and might be prone to break easily. Not nice.
The usual complaint about used strings is that they sound dull. But you have to ask whether they sound dull to you as the player, or dull to the microphone.
The sound heard by a well-positioned microphone on an acoustic guitar is hugely different to the sound heard by the player. For a quick test of this take your guitar close to a hard plaster wall and play it. The sound from the belly and sound hole of the instrument will be reflected back to you and you will instantly hear that it is louder, fuller and brighter than the way you normally hear it. Indeed, the sound might be exactly what you need for your recording.
There is no doubt however that strings are at their brightest when they are new, and they dull down quite quickly. So if you are recording a single-line solo that needs to be bright and shimmery for your song, then you might put on a new set of strings just for that solo, and hope to get it down within two or three takes. The brightness and shimmeriness - a characteristic I sometimes refer to as 'zing' - of new strings also works very well for finger picking where the texture is simple and open rather than complex and detailed. Where a maximum of two or three notes sound at once, then new strings can sound really good. Of course this is just my opinion and you should form your own. If you really listen closely the the sound of strings, then searching for an answer to the new vs. old debate on the Internet isn't relevant.
New strings have a 'zing' that works well for single-note lines and open-textured finger picking. Used strings would sound dull in comparison. Note the difference between 'used' and 'old'. Used strings can find application in an appropriate context. Old strings are hardly ever useful.
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