I changed the title of this second form in order to reflect the modern application. The Reformation was a reaction against the abuse of clerical authority. As new denominations formed in its wake, they sought a better way to counter potential abuses by distributing power among an eldership rather than in the hands of one person, which often emerged as a place of corruption.
Additionally, as they established the principle of Sola Scriptura, they began to rediscover biblical principles that seemed to point to a plurality of elders within a church and which also undercut the notion of a Pope who held authority over the Church. They still saw the need for governance, and thus introduced this new model which balanced power at multiple levels.
In modern times, many churches believe a plain reading of Scripture demands elder leadership within local churches, even if their denominational ties are not anchored in Presbyterian history. This is especially true amongst historic, Congregationalist churches as well as the new Reformed movement (Acts 29, etc).
Most mega-churches are led by elders, albeit with significant authority concentrated in the hands of a senior pastor. Very few of these elder-led churches also incorporate the graded courts of the full Presbyterian model. Gateway, Willow Creek, and Saddleback are all high-profile examples of this trend. They are Congregational outside the church, but elder-led/Episcopal inside the church.
Paul appointed elders after planting churches (Acts 14:23), he commanded both Titus (1:5-9) and Timothy (3:3-16, 5:17-22) to do the same and gave detailed instructions regarding how to do so. Acts 20:17-38 provides a gripping account of Paul’s farewell to the Ephesian elders and an exhortation for them to continue in their role. Peter likewise gave a broad instruction to elders across the Church in 1 Peter 5:1-11 (though the Episcopal model might claim this as applying to the bishops instead).
The Biblical support is so strong for eldership that both other models acknowledge the importance of this office but limit it to just one person per church (priest or lead pastor) rather than a plurality within a church, as well as disagree on the authority an elder holds.
Major variations exist within an elder-led structure, specifically in the appointment of elders and in the authority of the lead pastor. Some pastors serve as an employee under the elders’ direction, while others lead together with the elders (either as a peer or a leader among equals). Some elders are appointed by the pastor, outside apostolic council, or by the previous elders, while other models require the congregation to vote on the elders to serve as their representatives.
A full Presbyterian model would rely on the Jerusalem Council in Acts 15 to support their system of graded courts. They note that the elders of two churches joined together to make a binding doctrinal decision that applied to other churches who were presumably not present. Interestingly, the two most prominent apostles—Peter and Paul—submitted to this decision and did not exercise their apostolic authority to decide unilaterally. In fact, it seems James (not an original apostle) made the final decision together with the elders. To me, this should be a consideration, but is not prescriptive for the Church and appears to be a one-time occurrence rather than a formal system.
Elders embrace the wisdom found in a team comprised of diverse giftings while also avoiding the gridlock and politics imposed by a pure democracy. They also spread out the weight of ministry across multiple people and provide a model of Christian community to the church.
Elders functioning in the right way provide wisdom that cannot be found in just one person, represent the diversity of the local church, and bring a multiple of spiritual giftings to provide a richer leadership.
In a word: Conflict. An elder can create serious problems for a church and is often a primary growth barrier. It only takes one bad elder to sink a church, and an elder board provides a tempting opportunity for a power grab to undercut the lead pastor (if applicable).
Elders will also move more slowly and are more prone to politics than the Episcopal model, though not to the same extent as Congregationalism. Any model which places the pastor under the authority of the elders will generally stifle vision since the person executing and communication the vision lacks the authority to implement it. This will drive away apostolic leaders over time. Within a “leader among equals” system, authority can be confusing, and elders may default to an advisory role, which then creates a de facto “one-man rule” system.
Like Episcopalism, an elder team can wield authority to such an extent that it undercuts the ability to release the church into ministry. This team can emerge as an exclusive, elitist decision-making body if precautions are not taken.
In summary, I believe churches need some form of eldership and this is certainly a recent trend across denominations. The question is how the elders fit within the rest of the model—both an Episcopal model and a Congregational model can utilize elders, claim the corresponding scriptural support, and benefit from the pros of this system, while a purely elder-led model contains a lot of serious challenges.