My comments here are intended to be a bit provocative, in the sense of seeking to provoke a closer look at a phenomenon many of us may take for granted.
There are two ways to answer the question, "What is 'Western Buddhism'?": one definition concerns the phenomenon of convert Buddhism in the global north (the "west," or Europe and North America), where non-Asians whose families and cultures did not traditionally practice Buddhism convert to one or another Buddhist tradition. Convert Buddhist sanghas in this sense are necessarily sectarian to some extent, because you have new people becoming integrated with extant Buddhist communities that are themselves dispersed among different sects as a historical fact. This does not preclude good relations among different streams and traditions, of course. And it does not mean there are no significant differences between the practices of Western converts and those of their Asian counterparts, because there often are. My point is that the essence of the traditional practice is passed on. Consider the examples of
Chagdud Gonpa,
Kwan Um Zen, and of course the
Tendai Buddhist Institute: these are traditional schools who have accommodated themselves to North American logistics without compromising anything effective in the traditional pedagogy. The pedagogy works and we know this because these schools have achieved good results in students who have applied themselves to the practice. There are many other examples.
A second definition for "Western Buddhism" concerns the arising of a distinctly "western" form of Buddhism, a new tradition of practice by and for non-Asians ("novayana"). Here, the emphasis is on nonsectarianism, and sanghas are organized around the practice of meditation more specifically than the practice of traditional Buddhism as a complete methodology, as a whole. The leadership structure differs significantly as well: where traditional Buddhist schools are led by trained and ordained clergy or monastics, the "Vipassana Sangha" is often led by a layperson or is entirely absent of centralized or hierarchic leadership. This is, indeed, something new.
I am not convinced this trend is sustainable, however. By shedding any traditional affiliation or concern for doctrine or methodology and emphasizing in an egalitarian way the unity of all spiritual efforts, the sangha is left struggling to identify a clear sense of purpose or continuity. I have seen this happen to the extent that the mystical speculations of Carl Jung or Ken Wilber are treated as though they are as authoritative on the question of what Buddhism means as any traditional Buddhist text, and debates ensue over whether Paul Atrides or Yoda is a superior guide on the path. Similarly, in decoupling meditation from its role in a balanced Buddhist diet and making it the organizing principle of the sangha, an end in itself that needs no justification, meditation becomes available to any purpose at all: not a way to accomplish the bodhisattva's path but as a means to cope with your dysfunctional family and your crappy office job: lifestyle management rather than bodhisattva activity [more on this forthcoming]. To be clear, stress reduction in itself is fine, but it is not an end in itself for Mahayana practice.
My point is that in this form of "Western Buddhism," your method becomes whatever you want it to be, whatever you have at hand to fill in the gap, instead of a methodical engagement with your desires and the gaps of your learning. In the end, your teacher is a deluded person: you. And in a related irony, in the attempt to eschew the thicket of metaphysics by rejecting Buddhist methodological questions, the bus is driven much deeper into the weeds, into endless evaluations and comparisons of Meister Eckhardt and Joseph Campbell... perhaps these are interesting books, but they are more an avoidance strategy in this context than a shortcut around Nagarjuna or the sutras.
To sum all this up, the term "western Buddhism" is a contradictory one. It refers to at least two different kinds of practice, different kinds of motivation, different situation, arguably different cultures. A more systematic treatment of this question would be a useful project.
