from my small country in eastern europe, it seems that both 'analytic' and 'continental' philosophy are anglo-american-australian traditions. in this sense, 'continental' seems to be a label put on several directions in european philosophy - pretty different directions, by the way (phenomenology, critical theory, discourse theory all start from different assumptions and employ their methodologies to different goals).

i doubt, for example, that jean-luc nancy would identify himself as 'continental' - maybe more along the lines of 'post-phenomenologist'. and people who work in a broadly 'continental' approach - by anglophone standards - may have very little to say to each other, much like the 'analytics' and 'continentals' in anglophone universities.

from what i have read, it seems to me that the main way of doing philosophy 'the analytic way' seems to be arguing in favor or against a claim - which may or may not have its sources in previous philosophical texts. but for 'continentals' (if we preserve this label) argumentation is put along 'description', 'exemplification', 'proposing an alternative viewpoint', etc. (as some people in this thread also suggested).

maybe in this sense 'continentals' say that analytical philosophy seems pretty arid and limited - because their purpose and style are different, and find little relevance in what the proponents of the other tradition seem to do. but a 'derridean' in an european university may find just as irrelevant what a 'deleuzian' says - although their themes would seem pretty close to an 'analytic' eye :)

also, when i read nancy or levinas, their way of doing philosophy seems pretty different than that of a lot of their american interpreters - in the secondary literature, i have found expressions such as 'levinas' argument seems to be...' in moments where i or my department colleagues would not interpret levinas' text as an argument at all :) - a kind of translating their texts in a more 'analytic' language and modifying them to suit analytic purposes.

so, it seems to me that 'analytic' and 'continental' traditions have developed mostly on anglophone soil - but from different sources - and may be closer than some of their main figures are caring to admit.

as to the reasons of this divide - i know too little about the climate of the american academia to say anything justifiable :)