Could this also be translated as "antique"? Ancient sounds kind of weird to me in this context.
cổ is a Sino-Vietnamese word (chứ hán) whereas cũ is not (chứ nôm). Sino-Vietnamese words are often perceived as fancier or more civilized. though they both mean "old", "ancient", my very own perception is that sthg is cổ when it is ancient, antique yet could be in good condition; cũ has this feeling of old stuff, not so good in shape or second-handed.