There are no unbiased authors. And Catholics don’t write much about this, except for people with strong polemical agendas.
A good general book on Protestant history, though with a strong Protestant bias, is Alister McGrath’s
Christianity’s Dangerous Idea.
Nathan Hatch’s
The Democratization of American Christianity is a great survey of the Second Great Awakening and the development of free-church American traditions–he has chapters on both the Campbellites and the Mormons.
Mark Noll’s
America’s God covers 19th-century American Christianity in more detail but with less emphasis on the development of specific traditions and more on the political and cultural ramifications.
The magazine my wife edits,
Christian History, did an
issue on the Campbellites a year or two ago and is doing one on the Methodists now.
Edwin