I can imagine that it may often be difficult for responses on philosophy.stackexchange to be correctly called 'answers' since there must always be room for interpretation and evaluation in philosophical matters, but allow me to give you my views on your question and from it perhaps you will be able to discover an answer for yourself if not for everyone.
Continental philosophy has profoundly—albeit misguidedly—influenced art, literature and film throughout the world. Analytic philosophy has inspired developments in mathematics and computer science, shaped the scientific method, and informed quantitative approaches to psychology and sociology. Both branches have elicited developments in linguistics. What continental philosophy has not done is continue developing in its original spirit; even since Sartre, continental philosophy has rather begun to regress or become blended with analytic flavours, with such notions as embodiment blending ideas from Kant, Husserl, Heidegger, Merleau-Ponty and others. Conversely, analytic philosophy has continued developing in the same way but in increasingly insignificant increments as it gradually cedes much of its original lines of inquiry to the sciences.
This is the primary distinction between the two branches of philosophy: analytic philosophy walks hand in hand with science and scientism; continental philosophy focuses on the poetic and metaphysical understanding of the world. Analytic philosophy divides the world into subject and object; continental philosophy seeks to unite observer and observed to reach a fundamental and unbounded picture of both. Analytic philosophy seeks to simplify philosophy through demarcation, whilst continental philosophy is concerned with questions that are intuitively more fundamental even than science or logic.
Analytic philosophy might be said to have had the more profound influence in contemporary academic circles, but what does that actually mean? Analytic philosophy has no purpose, because its goals are either impossible or fall to scientific endeavours to complete. Continental philosophy has arguably seen less academic attention (or at least less academic understanding/improvement) but the ideas of phenomenology, existentialism and deconstruction have disseminated globally and inspired vast amounts of creative work—though often the ideas are distorted or misinterpreted in such works, as is usually the case when an academic concept reaches the populace.
Judging which branch of contemporary philosophy has had the more profound influence will depend on what you personally think is more profound: the sciences or the humanities. Or perhaps not, if you think as I think: that analytic philosophy is not philosophy at all, but rather an auditing process for scientific enterprise. Continental philosophy represents, to me, a truer philosophy, especially through Heidegger and the break with the Cartesian tradition of subject/object opposition and through Derrida's subsequent refinement of destruktion as deconstruction.
Within the academic discipline of philosophy itself, it is difficult to judge which branch had the more profound impact. Philosophy finds itself in troubled water these days, unsure of whether it is a science or an art; you will find academics undertaking scientific studies of a psychological/neurological character calling it philosophy, and likewise you will find people still agonising over Aristotle, Chrysippus, Kant, Hegel, Husserl, and so on—and as Derrida certainly demonstrated, no philosophers will truly lose their significance, because their ideas were defined and remain defined by their opposition to each other and to the times, and that these definitions are traces of a genealogy of meaning that will not end.
We might say that Continental philosophy affirms philosophy as a subject and gives it life, paves the way for future study and creation. In contrast, analytic philosophy might be said to be less constructive, narrowing philosophy down according to scientific standards over which philosophy ought to preside. I do not mean to say that analytic philosophy is only logical positivism, but analytic philosophers do not do what philosophers must by definition do: question themselves and their methods.
