Both have the same meaning: "That star is you." But what makes them different? If it's the nuance, what exactly is it?
Context: It's from a song's lyrics, the first one get sang first, whilst the latter get sang later.
だ is the basic form of the copula, so あの星はあなただ is a complete sentence.
で is the continuative form of だ, so あの星はあなたで is not a complete sentence; it leads into whatever follows.
Basically あの星はあなただ is simply "That star is you", whereas あの星はあなたで is more like "That star is you, and..."