"In this ‘Australian School’ of thought, Ediacaran fossils have generally been defined in terms of their differences from each other, while their biological affinities have been argued by means of analogous reasoning with respect to the similarities with extant invertebrate groups"
"Such an odd situation is inherently unstable, and an alternative view therefore began to emerge within what we shall here call the ‘European School’ of thought, so-called herein because these views originated from scientists working in Europe. We do not mean to imply agreement amongst the ‘European School’ as to the placing of the Ediacara biota within the modern phyla. Instead, we draw attention to the tendency of this school of thought towards thinking that the Ediacara biota may be more closely related to each other than to any modern groups."
What can i say? Brasier's identified two fairly real strains of thought in palaeontology. I don't credit him with any originality there. You often come across a brief note at the beginning of papers in this field, highlighting the differing interpretations of the Ediacaran fossils in a similar way. In fact, Stephen Jay Gould wrote a whole book about it, though he was talking about a different set of fossils. Usually it's presented like this: we used to think these fossils were all related to modern forms, lately people have been questioning that.
All Brasier's brought into it is a geographical division. The "we used to" is the 'Australian School', the "lately" is the (more refined?) 'European School'. Other researchers might talk about "lumpers" v "splitters", or the practise of "shoehorning" extinct animals into recognisable modern forms v. a more imaginitive paradigm of treating them as potentially new phyla - but Brasier's given us the 'Australians' v 'Europeans'!
The philosophical division is real, but the choice of labels is a bit off (and could easily be taken the wrong way... i wonder if they're being deliberately provocative?). Although, re-reading Gehling's (Australian) chapter in "The Rise of Animals", he does explicitly identify an "Adelaide" school, exemplified by himself, Wade, Jenkins and Glaessner. But he also emphasises that Wade & Glaessner were "fully aware that many Ediacara forms were not related to any of the living animal phyla".
And the early work by Gurich and Richter certainly represented attempts to classify Ediacarans as members of modern groups. And they were writing from Germany, about Namibia. Hardly 'Australian'. And hardly what Brasier and Antcliffe identify as the 'European' school. You could probably trace the entire 'European School' to two particular people, Pflug (who placed certain Ediacarans in the new phyla Petalonamae) and Seilacher (who placed them in the Vendobionta).
As for identifying Ediacarans by their similarities to each other (Brasier & Antcliffe's 'European School') rather than their similarities to modern groups (us ignorant 'Australians' ;) ), aside from the initial peices by Pflug and Seilacher, there hasn't been a great deal of work from any 'School' advancing this perspective in as much depth as it deserves. I suspect this division has more to do with the early Ediacaran reports coming from Australia simply because the Ediacarans were first identified as a unique fauna in Australia, and later reports (more open to novel interpretations by virtue of coming later) mainly appeared after the identification of Namibian (German), Canadian, and Russian sites as being Ediacaran, when a new set of researchers became interested.
But i'll read through the references, and give them a hearing. With a smirk on my face, i'm sure.