The answer will vary with different bird species as well as with different bird owners, so you will have to decide for yourself and your birds.
You should find out as much as you can about the nutritional needs of the species that you will (or already own) and do your best to meet those needs. Unless you live in the country that your species originates, it is unlikely that you will duplicate the diet of this bird in the wild, but you can come close to the nutritional needs using locally available foods.
Of course, there are more options than seeds or pellets and it doesn't have to be one or the other. It can (and probably should) be a mixture, but not just pellets and seeds. Nuts, fruits and vegetables can be added into the mixture or fed at different times of the day. Fruits and vegetables can also be the full diet of many birds.
You can also cook or bake for your birds. Bean mixtures are a healthy treat that can form a good part of many birds' diets. Birdy bread is another healthy favourite for many birds that are lucky enough to have someone bake for them. You can find recipes for these items easily online by searching or by following the link below to Bird Foods. There are even some e-mail lists that are devoted to feeding your bird.
If baking or cooking for your bird is not something you are able or willing to do, you can also purchase these items online or directly from some pet stores.
Some birds, especially the smaller birds such as budgies, canaries and finches live long healthy lives on a strictly seed diet, while other birds live long healthy lives on a strictly pelleted diet. If your bird is eating only one or the other, it would be good to introduce other foods, but do not worry if your bird does not immediately recognize other items as food.
If you decide to change your bird's diet, please do not remove the old food immediately because birds will die of starvation rather than eat something that they do not recognize as food.
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