This question came up as part of an on-line discussion group AND it caught my attention as I've been reading Carlton O. Wittlinger's Quest for Piety and Obedience in preparation for the August Brethren in Christ History and Values course taught by E. Morris Sider (Note: more from the course as I get to it). Here's some material from Wittlinger's Quest for Piety and Obedience which I shared:
1. The Brethren in Christ originated about 1780 along the Susquehanna River near the present town of Bainbridge in Lancaster County, Pennsylvania (p.1).
This is of interest because the Mennonites were "followers" of Menno Simons (who became Anabaptist in 1536) in the Netherlands and emigrated to William Penn's "Holy Experiment." So there is a span of about 250 years between the founding of the Mennonites and the Brethren in Christ.
2. With regard to the Brethren's [i.e., Brethren in Christ, BIC] beginnings, differences existed with the Mennonites in the areas of baptism and conversion. Trine baptism was/is considered the biblical mode by the BIC and conversion stands in the Pietistic tradition (with the Dunkers who were founded in 1708 in Schwarzenau, Wittgenstein, Germany by Alexander Mack).
Affiliation with the Mennonites, another theoretical option, was never a serious possibility, although the two groups agreed in many respects on the meaning of obedience. Both viewed baptism as an act of symbolic commitment to the Christian life, but they disagreed on the mode of ordinance. The Mennonites baptized by pouring following the precedent of European Anabaptism. Commitment of the Brethren to trine immersion might have been sufficient to prevent their fellowship with the Mennonites.
More important than baptism, however, was the fact that the Mennonites, like the Dunkers [currently known as the Church of the Brethren], did not regard a personal, heartfelt experience of the new birth as normative for the beginning of the Christian life (p.23).
3. As the founders of the River Brethren, which gave birth to the Brethren, came principally of Mennonite background (p.21), one might consider the Brethren a Mennonite revival movement [note: my term], influenced by Dunker and United Brethren in Christ pietism. At times, [t]he early Brethren were occasionally called River Mennonites because some of their first ministers [including Jacob and John Engel, John Greider, and possibly John Winger] had been connected with the Mennonites (p.18). Earlier Wittlinger discusses Alexander Mack's, a Dunker, critique of the Mennonites, they have deteriorated in doctrine and life, and have strayed far from the doctrine and life of the old Baptists [Anabaptists]. Many of them notice this and realize it themselves. Note: in addition, Mack critiques the lack of trine immersion (p.8).
To follow the story of the influence of Pietism, Wesleyan Holiness, and Evangelicalism upon the Brethren in Christ, which for the most part is lacking among the Mennonites, I'd recommend Luke Keefer's Brethren in Christ: An Uneasy Synthessis of Heritage Streams (an edited version his article The Three Streams in Our Heritage: Separate or Parts of a Whole? in Brethren In Christ History & Life XIX:1 (April 1996), 26-63).
As the Mennonites have largely not traveled this path, they remain more communal/familial than the Brethren in Christ (although in Lancaster County, PA, this remains strong) and more Anabaptist than Evangelical. But all movements ebb and flow with regard to intensity of devotion and steadfastness not only to specific individual and communal practices, but also perspectives. The passing of structure and direction from generation to generation, across time, geography, and culture has proven complicated for all religious groups. By-the-way, I have good relationships with both Mennonites and Brethren-in-Christ even though I did not grow up either tradition. Note: Theresa's family is largely Mennonite and Brethren in Christ.
For current day, compare the Church Member Profiles for the Brethren in Christ (in PDF) and the Mennonite (in book form, which I've not read, but I heard Conrad Kanagy's presentation at Elizabethtown College) denominations. Note: a general history of the Brethren in Christ without reference to the Mennonites can be found on the Brethren in Christ website.
Commonalities to be stressed, in addition to the shared Anabaptist heritage, are that Mennonites and BIC remain Historic Peace Churches and partnerships exist with a number of ventures including Mennonite Central Committee (founded 1920, which includes Ten Thousand Villages), Mennonite Distaster Service, Mennonite Mutual Aid (MMA), and Mennonite World Conference (founded 1925). Note: Danisa Ndlovu, bishop of the Zimbabwe BIC church is president-elect of Mennonite World Conference, see Brethren in Christ article.
That's all for now. Would love to read the thoughts of others.