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Solid wood is going to last you way longer than melamine, but it all depends on how you take care of it and what type of wood it is. If your wooden furniture is well treated, sealed, and you don't expose it directly to heat or humidity, it can last you decades. Melamine, which is particleboard covered with a plastic film, typically lasts between 5 and 15 years max before it starts to delaminate, swell, or chip along the edges. The bad part is that once it's damaged, it's practically impossible to repair decently.
That said, durability also depends a lot on the initial quality. Softwood like pine or birch doesn't age the same way as hardwood like oak or walnut. And cheap melamine from some fast furniture stores deteriorates way faster than the stuff from brands that use better board. If your house is humid or you've got kids constantly sticking things on the furniture, even wood can suffer.
My recommendation is that if you're going to invest in something you want to last, look for solid wood or at least decent quality plywood. Yeah, it costs more, but you get your money's worth over time. And if you go with melamine, do it if you know it's temporary or if you really can't afford anything else. But once the melamine starts to fail, you'll already be looking for another piece of furniture.
Melamine is going to peel and delaminate pretty quickly if you expose it to humidity or temperature swings, but solid wood isn't a guarantee of durability if you don't take care of it - I've seen cheap pine furniture that splits after a year. What really matters is the quality of the material and the finish, because even good-brand melamine lasts for years if you keep it dry and don't bang it up. That said, yeah, wood is structurally more resistant over the long term, but it's not as dramatic a difference as some people think.
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