Is it more preferable, immediately after the Adhan – that is, after saying "Allahumma Rabba Hadhihi Ad-Da'wati At-Tammah" – to make supplication or to pray?

A Muslim says what the mu'adhdhin says, then invokes blessings upon the Prophet (peace and blessings be upon him) and asks for al-Wasilah for him. He then prays two rak'ahs between the adhan and the iqamah, and strives in supplication, which is not rejected, between the adhan and the iqamah. There is no evidence to suggest that one of these actions should be given precedence over another. However, prayer is the best subject and includes supplication, so it might be given precedence.