Wooden recorders tend to have a more "authentic" recorder sound, but it's not always better. For example, you're probably better off with a higher priced plastic recorder instead of a lower priced wooden one. If you have plenty of money, though, a higher-priced wooden one will very likely sound the best.
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Naturally, there are different qualities of both wooden recorders and plastic recorders, but, mutadis mutandis, all else being equal, wooden recorders sound much different from plastic recorders and are much superior to plastic recorders. They are also, unfortunately, almost invariably more expensive than plastic recorders. I have no trouble affording a wooden sopranino or soprano recorder, but I've been slightly daunted at the cost of a wooden alto recorder, more daunted at the cost of wooden tenor recorder, and completely taken aback at the cost of a wooden bass recorder.
In music class we have been playing recorders! We use Yamaha plastic recorders and they sound beautiful! The wood might sound nice if it's higher priced but I suggest you go with plastic because they have a clearer sound and a little less diffuculties.