Occasionally, I find myself party to conversations about analytic and continental philosophy. It seems to me that Socrates, Plato, Aristotle, Sextus, Augustine, Boethius, Anselm, ibn-Rushd, al-Ghazali, Maimonedes, Aquinas, Scotus, Ockham, Descartes, Spinoza, Leibniz, Locke, Hume, Kant and Frege all practiced analytic philosophy for a significant part of their philosophical lives—some of these, indeed, for just about all of their philosophical lives. When I read these people, I find them kindred souls, clearly engaged in the same rational pursuits, using pretty much the same tools, as I am. To denigrate analytic philosophy would, thus, be to cut oneself off from much of our philosophical tradition, and to lack the tools of analytic philosophy is to severely limit one's ability to engage this tradition. Fortunately, I have found it rare these days for continental philosophers to denigrate analytic philosophy.
I presume continental philosophers can likewise trace their lineage through the history of Western philosophy, though some of the names will be different. Significantly, I expect that just every major figure in the middle ages will have to be left out, and perhaps also Aristotle (but Plato and Socrates would stay), but one can in exchange add a number of more recent luminaries like Pascal, Hegel and Kierkegaard. By and large, continental philosophy strikes me as a more recent development. (Nothing wrong with that!)
I worry a bit about unconsciousness of ignorance. I am basically entirely ignorant of continental philosophy. Yet it does not seem to me that this ignorance significantly hampers my understanding of any pre-20th century philosophers I've read with the possible exception of Husserl. I presume that likewise continental philosophers who do not know any analytic philosophy do not think they are missing out on much understanding of major historical figures. So, I guess, I should conclude that probably I am missing out on major insights through my ignorance. On the other hand, maybe we're all lucky, and the insights about, say, Plato and Ockham that I'm missing by ignorance of continental philosophy are not insights I am that interested in, and the insights about them that the continental philosopher ignorant of analytic philosophy is missing out on are ones that she is not that interested in. But this doesn't seem right—philosophy is, surely, properly a holistic enterprise.