Chrysostom on Peter:
“…He [Jesus] brought him [Peter] back to his former honor and entrusted him with the headship of the universal church, and, what is more than all, He showed us that he had a greater love for his master than any of the apostles, for saith he: ‘Peter, lovest thou Me more than these?’”
“He saith to him, ‘Feed My sheep.’ Why does He pass over the others and speak of the sheep to Peter? He was the chosen one of the apostles, the mouth of the disciples, and the head of the choir; for this reason Paul went up to see him rather than the others. …He entrusts him with the rule over the brethren…”
“If anyone should say ‘Why then was it James who received the See of Jerusalem?’ I should reply that He made Peter the teacher not of that See but of the world.”
(Yes, yes, John and Paul are also called teachers of the world. Just goes to show that at a certain point Peter didn’t need to hold a see to “rule over the brethren”.)
“In those days Peter stood up in the midst of the disciples and said: 'as being fervent, and as having the flock entrusted to his care, and as the first of the choir (or, as preferred in honor) he is always the first to begin to speak.”
"‘And in those days,’ it says, 'Peter stood up in the midst of the disciples and said: Both as being ardent, and as having been put in trust by Christ of the flock, and as having precedence of honor, he always begins the discourse. …Wherefore at the beginning he said: ‘Men and brethren, it behooves us to choose from among you.’ He defers the decision to the whole body, thereby making the elected objects of reverence, and himself keeping clear of all invidiousness with regard to the rest… …why did it not rest with Peter to make the election himself? What was the motive? This: that he might not seem to bestow it of favor. And, besides, he was not yet endowed with the Spirit. …[Peter] did not say: ‘We are sufficient.’ So far was he beyond all vain glory, and he looked to one thing alone. And yet he had the same power to ordain as they all collectively.
(So he was sufficiently “empowered” to choose Judas’ replacement himself, but chose not to.)
— How can one be in charge over others yet be equal to (or the same as) them at the same time? This is possible, but one has to recognize different levels or senses of authority and honor. So Peter is the same as the others in that all were Apostles, but not all Apostles were equal:
“In the Kingdom, therefore, the honors were not equal, nor were all the disciples equal, but the three [Peter, James, John] were above the rest; and among these three again there was a great difference… And yet all were apostles, all will sit upon the twelve thrones, and all left their possessions, and all were with Christ. And yet he selected these three. And, again, among the three, He said that some must yield or excel. For, ‘to sit on My right hand and on My left,’ he said, ‘is not Mine to give, but to them for whom it is prepared,’ And He set Peter before them saying: ‘Lovest thou Me more than these?’ And John loved Him more than the rest.”
All sourced from PhilVaz’s site (again).