Like "race", the concepts of "nationality" and "national identity" are very modern; these terms would have meant nothing to the peoples of Antiquity. However, even if we rephrase your question as "what was more important to ancient people's sense of identity, physical characteristics or ancestry", the answer is still a mathematician's "yes", because you've included sexual characteristics under visual cues. Discrimination in terms of exclusion from legal and political rights was on grounds of ancestry and sex (that is, both intangible and tangible factors). Both the Greek city-states and the Romans based their definitions of citizenship almost entirely on parentage (with the remaining factor being wealth), but only men were allowed to participate in politics, war, the judicial system, etc. As long as you could prove that your mother and father were Athenian citizens, you were an Athenian citizen - but only male citizens had full citizen rights.

On the other hand, there was no sense in which visual cues distinguished citizen from non-citizen. One Greek author complained that it was impossible to tell freeborn citizen from slave at Athens, because they dressed the same - showing that there was no concept of citizens being distinguished by certain physical characteristics. In this sense, discrimination was by ancestry only.