In ancient history currency, coinage, got their value from their composition. A gold coin was still made of gold so it still had value. Yes, ideally the conquers would want to melt the coin down and reissue it featuring the conquer's head and symbols but if it was not a big enough deal to take the coin immediately out of circulation or refuse to accept it.

Confederate money became worthless because it was made of paper, it has no intrinsic value. The value comes from a guarantee from the Confederate States of America, without the C.S.A. it has no value.

TL;DR Ancient coins worth came from the intrinsic value. Confederate money, overwhelmingly paper, has no intrinsic value.