Classic and Classical are not the same in English, though the same word in Portuguese may mean either, depending on the context. Classical is more restrictive and has more historical connotations. First of all, classical and "classics" without a context refers to ancient Latin and Greek art and literature or their study. In music, "classical" music is specifically "concert music," "art" music. Sometimes in other contexts, such as "classical economics" or "classical physics," it has the sense of "academic," sometimes "traditional" or "standard." The Adjective "Classic" and the noun "classic" can be used to refer to almost any work of art, popular or classical, or fashion, even a joke, that is, as above, a model example or a work or style that is long-lived, not ephemeral. You might say "classic rock and roll," but not "classical." The meanings overlap somewhat, but usually the words are not interchangeable.
My first thoughts about "O chapéu dela é clássico" was indeed of a classical model hat, i.e. a model hat from a previous period. So if I understand well, that could be the meaning of the Portuguese? And in that case would "classical" be the proper translation? In fact I didn't know the word "classic".