This, Murcielago, is a very interesting question.
I tend to think of the "ministries" as completely different, and because there is president, ministers, pastors(as it applies to modern times) can get paid to do ministry full time, as the priests did. I see pastors ministry more closely related to that of the priests, as they both had/have to deal with the day in and out of the spiritual needs of the people. Jesus, resembled more in the line of an evangelist, where he came to town had a meeting, etc. and moved to the next place. Both I feel are very necessary to reach people, as people are reached in different ways. I am not sure but I don't believe there were "formal" groups formed(other than His disciples) that followed the teachings of Jesus, until after his ascension. There were supporters everywhere He went, but the multitudes just seem to follow Him where ever He went, or when they heard He would be a certain place.
All that said, I do understand you point, that maybe the priestly system was part of the "law" also fulfilled by Jesus, if we think of His current work in the Heavenly sanctuary. That would most definitely leave current pastors, evangelist, etc. to follow more the example in ministry of Jesus and the disciples/apostle, and minister wtihout pay.
Another point to be made is that Jesus ministry was intentionally shortlived, but then that of the apostles was not.......quite a quandry, indeed! LOL!!