Assalamualaikum ustaz. Can you explain which is prioritized between a bilal and an imam?
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions and all those who follow his footsteps until the Last Day.
Imam means a person who is followed for he has several commendable characteristics such as kindness, obedience, bravery and knowledgeable.  Imam also means someone followed by others, such as the imam for prayer, as a caliph, or commander in battle. 
The word imam itself means in the front, referred to and followed while his follower is known as the makmum. This is based on a hadith of the Prophet PBUH:
اِنَّمَا جُعِلَ الإِمَامُ لِيُؤتَمَّ بِهِ
“The imam is appointed only to be followed,” 
Indeed, it is obligatory for the makmum to follow all the actions of the imam, such as takbir al-ihram, prostration, iktidal and others.  All the actions must be performed by the makmum after the imam performed them. If the acts are done by the makmum before the imam, then his prayer is invalid. 
As for the adhan, it is one of the greatest eminences of Islam. In syarak, it means specific phrases called out to inform that the time for the five obligatory prayers has begun. This is based on a hadith narrated by Malik bin al-Huwairith. He said:
أَتَيْتُ النَّبِىَّ -صلى الله عليه وسلم- أَنَا وَصَاحِبٌ لِى فَلَمَّا أَرَدْنَا الإِقْفَالَ مِنْ عِنْدِهِ قَالَ لَنَا إِذَا حَضَرَتِ الصَّلاَةُ فَأَذِّنَا ثُمَّ أَقِيمَا وَلْيَؤُمَّكُمَا أَكْبَرُكُمَا
“I came to the Messenger of Allah (ﷺ) along with a companion of mine, and when we intended to return from him, he said: When there is time for prayer, announce prayer, pronounce Iqama, and the oldest amongst you should lead the prayer.” 
Imam al-Nawawi said this hadith is evidence of the obligation to always protect the eminence of adhan whether one is on his travels or at his place of residence. 
Adhan is a specific dhikr. Islam sanctions it to inform the beginning of the obligatory prayer times and call the Muslims to pray together. Iqamah is the same as adhan with several differences, such as the phrases in the adhan is called twice, while iqamah is just once. 
Which is Prioritized or Better?
This is a khilaf issue among scholars.
First: According to the sahih opinion from Syafi’i and Hanbali scholars, adhan and iqamah are better than being an imam. This is based on the statement of Allah SWT:
وَمَنْ أَحْسَنُ قَوْلًا مِّمَّن دَعَا إِلَى اللَّـهِ وَعَمِلَ صَالِحًا
“And who is better in speech than one who invites to Allah and does righteousness…” 
‘Aisyah R.Anha said, “The person meant in this verse is the muezzin.”
Numerous hadiths state the advantages of calling the adhan. Among them is the statement of the Prophet PBUH:
لَوْ يَعْلَمُ النَّاسُ مَا فِي النِّدَاءِ وَالصَّفِّ الْأَوَّلِ ثُمَّ لَمْ يَجِدُوا إِلَّا أَنْ يَسْتَهِمُوا عَلَيْهِ لَاسْتَهَمُوا
“If the people were to know what excellence is there in the Adhan and in the first row, and they could not (get these opportunities) except by drawing lots, they would have definitely done that.” 
Rasullullah PBUH also said:
فَإِذَا كُنْتَ فِي غَنَمِكَ أَوْ بَادِيَتِكَ فَأَذَّنْتَ بِالصَّلَاةِ فَارْفَعْ صَوْتَكَ بِالنِّدَاءِ فَإِنَّهُ لَا يَسْمَعُ مَدَى صَوْتِ الْمُؤَذِّنِ جِنٌّ وَلَا إِنْسٌ وَلَا شَيْءٌ إِلَّا شَهِدَ لَهُ يَوْمَ الْقِيَامَةِ
“So, when you are looking after your sheep or when you are in the desert and want to pronounce the Adhan, raise your voice, for no Jinn, human being or any other things hear the Mu`adh-dhin’s voice but will be a witness for him on the Day of Resurrection.” 
In another hadith, it is stated:
الإِمَامُ ضَامِنٌ وَالْمُؤَذِّنُ مُؤْتَمَنٌ ، اللَّهُمَّ أَرْشِدِ الأَئِمَّةَ وَاغْفِرْ لِلْمُؤَذِّنِينَ.
“The imam is responsible and the mu’adhdhin is trusted, O Allah, guide the imams and forgive the mu’adhdhins.” 
Responsibility is higher than dhaman while forgiveness is greater than guidance. Prophet Muhammad PBUH and the caliphs didn’t bear the responsibility of calling the adhan because they don’t have much time.
Second: According to Hanafi scholars, iqamah and being an imam is better than adhan for Prophet Muhammad PBUH and the caliphs were all imams but they did not become the muezzin. 
Our opinion is the same as the jumhur and madhhab Syafie based on the apparent meaning in the hadiths. Furthermore, there are too many advantages for calling out the adhan and iqamah. However, we can never deny the advantages of an imam as the leader in the worship of congregational prayer.
May all of us get to receive the advantages of being an imam or muezzin or even a makmum. Amin.