Things smakar "adverb" in Swedish, but taste "adjective" in English. It's the same with smells.

There's no real difference, and both are very common. I'd say gott is probably more common and a little more idiomatic.

There are no neuter/common forms of adverb gott. I don't know why we don't use adverbs in the modern English version of this, but it would be like "It tastes goodly" if we did. Centuries ago, that would have been a fine way to say it. In fact, "It tastes badly" still sounds OK despite no longer being standard.
Adjective versions like "It has a taste which is bad." or "Its bad taste was too strong" in which taste is standing in for the noun flavour could translate to a Swedish sentence with adjective gott/god, but not with the verb tastes because verbs are supposed to be modified by adverbs. It just so happens that the Swedish adverb form is usually the same as the neuter adjective form and adverbs don't get declensions for the verb they modify. They have one form. Or perhaps you could think of it as all verbs are ett words, because gott is modifying smackar. It is not modifying korven at all. (Although, I think goodly-er and goodly-est don't look like neuter forms in Swedish, so scratch that thought).