With the intent of translating this sentence to Latin, what case is the word "fame"?
In your title you ask if "fame" is a predicate nominative, and the answer to that question is no. A predicate nominative involves the linking of a noun with the subject via a copula (usually a form of "to be" or "to become").
Based on the body of your question, I suspect that your real question is what case would best be used to translate fame. The answer is that you have two options.
Same case as compared noun = nominative
Gloria melior est quam fama.
Ablative of comparison
Gloria famā melior est.
The two are both equally valid, though the ablative is often avoided in cases where ambiguity could arise. In this particular case, I would probably favor the first option because my ear isn't sensitive enough to vowel quantity to intuitively understand the second when spoken.