There's some basis for lumping birds in two piles but it seems to be a beauty-contest judging call.
Interesting link. I was expecting that the ratites (ostriches, et al) might be a much older group than the volants (flyers), but no such neat divisions seem to appear.
Also, it appears that Feduccia has had his nose in this issue right along:
Whether modern birds are most closely related to dinosaurs or crocodylian ancestors is a point of current debate. The orders of extant birds appear to have arisen close to each other in time, although their age is uncertain, having been estimated to be about 60 million years old or over 90 million years old based on morphology and fossils (see Feduccia, 1996) and molecular data (Sibley and Ahlquist, 1990; Hedges et al., 1996), respectively.