First of all, this question is a part of a broader question, regarding the general relationship between philosophy and politics. Once it has been defined, however tentatively, it would be possible to probe further into the inner-relationship between kinds of philosophies, and their relation to politics. Then, in a third part, the issue of helpfulness could be addressed. So any attempt to understand the relations between philosophy and politics must begin with some (presupposed) understanding of what philosophy is. This question, as old as philosophy itself, is never neutral; but, already presents a philosophical position. Differently put, there is no neutral definition of philosophy, which is not at the same time a position within the field of philosophy. Thus, to say that "philosophy is such and such", already signals a position within the philosophical field. And the same holds politics: there is no neutral definition of the field of politics without taking an engaged position from within this field. For example, to define right and left, is already a leftist or rightist position.
Our definition of philosophy will shape, to a certain extent, our portrayed relationship with politics. Let us first introduce the distinction between politics and philosophy. The former is a truth-procedure, the latter is the study of that conditional procedure which in turn links a subject to truth. Philosophy, in itself, has nothing to do with truths. For this, we have science, art, love, and, well, politics. These procedures produce truths in the world. Philosophy is the study of these procedures, without which there was no philosophy whatsoever. And while politics or science can only show us, people and societies, what truth is (in a form of a theory or revolution), it is philosophy which creates this link between a subject--an embodied way of life--and that very truth. This already attests to the initial relations between philosophy and politics (regardless the various kinds of philosophies exist). Politics produces truths, philosophy links them with a subject.
But how do different kinds of philosophy address and articulate, let alone enact this link? And what are the different implications? Here, it should be noted that the distinction between continental and analytical is misguided. First, because it involves two terms from different categories: continental is geographical, and analytical is scientific. To correct this we should either say American and European, or synthetic (speculative) and analytic. Second, and more importantly, the diagonal move between these two categories (the move that created the continental-analytical division) is so prevalent only to hide its point of inconsistency: there is analytical within the continental, and continental within the analytical. Namely, their border is totally blurred. For example, analytic philosophy started in Europe, with Logical Positivism and figures such as Moritz Schlik and Rudolf Carnap, not in the states. Its origins are profoundly European (for better or for worst). And within the continent of Europe (for now), England is a great supporter of the analytic school, opposed to the more continental-oriented France and Germany. We see that the analytic-continental division is not a very useful one, even before we come to politics. Instead, and beyond geographical delineations, I will use the distinction between analytic and synthetic (or speculative)--themselves topological spaces--and claim that you can find both tendencies in any country or continent.
Now let us examine the relationship between each tendency and its relation to politics, defined as a truth-procedure. Here, first, we must define the two tendencies in order to start seeing the contours of the political affiliation of each. What is analytic? what is synthetic? Or rather, what is the thing which is either analytic or synthetic? To put a very long story short, it refers to the Kantian philosophical revolution. Revolution, since Kant himself described his (critical) work as having the same status and implications of the Copernican revolution. Just as Copernicus decentralized earth as putting the sun (or heliocentric thesis) in the centre, Kant decentralized the object (any object) by putting the subject (and its transcendental categories) in the centre. Even more so, Kant was able to posit that categories (of the transcendental) are the boundaries of human thought, as they limit our grasp of the thing-in-itself and allow us to know only the thing-for-us (as it appears to an 'external' observer). In his Critique of Pure Reason (1781), Kant distinguished between two kinds of propositions: Analytic and Synthetic. The former are statements which contain their own truth value while the latter are statements which do not hold a truth within them. He then introduced temporality, time, into the picture: Analytic a-postriori propositions are impossible. Synthetic a-postriori are empirical statements (it will rain tomorrow). Synthetic a-priori are knowledge statement (7+5=12). And analytic a-priori are tautological (all singles are unmarried).
In this way, Kant showed how layers of reality can be separated by analysis, like a surgeon separating layers of flesh with a scalpel, or, alternatively, it can be sutured, stitched together as a chemical synthesis. This process, in philosophy, relates to logic and phenomenology--the study of appearances--as how things appear to us is greatly determined by our symbolic (linguistic and discursive) categories which are, in effect, a logical space prescribed by some logical setting (matrix of laws). And in Logical Positivism they radicalized Kant in such a way, that not only eliminated his true insight but created a path to "analytic philosophy" altogether. While Kant excluded only analytic a-postriori statements, because how can something that holds its truth within it be dependent on time?, in Logical Positivism they excluded also synthetic a priori statements, for being impossible. For them, opposed to Kant, this kind of statements, like "7+5=12", are true in themselves, regardless of the proof provided by our use of the faculties and categories of Reason.
What Kant regarded as synthetic, they considered as analytic (by radicalizing Hume's induction problem, the inability to conclude real, eternal and a-temporal (analytical) laws from time-dependent observations). This very move is the condition of possibility of Analytical philosophy, of which the basic premise is that truth resides inside (and can only be accessed through) language, once distilled from all practical influence of ambiguity, multiformity. This idealization of language resulted in a form of universe devoid of dialecticty. Because of the (Aristotelian) idea that truth is a logical adequation between words and things, thoughts and worlds, the dialecticity of truth as the immanent "tarrying with the negative" (like Hegel has put it in his 1807 Preface to the Phenomenology of Spirit) process of its development, was eliminated. Against this negativity of the dialectics, there was Logical Positivism.
However, other schools of thoughts have developed the Kantian revolution in different forms. Actually, most of non-analytical philosophies are such further developments: the Heideggerian ontological phenomenology, or The Deleuzian vitalist approach, or the Jamesian pragmatist approach celebrated in the US. And so it is not just analytical and synthetical. The even more crucial distinction to be made here, since we are approaching politics, is the relation to negativity and positivity. Negativity is looking, studying, and ultimately realizing what is not in language/reality, and yet, as truth, effects reality precisely by being outside of it. Thus, if we take politics to be about the change of our social representation, then the question of negativity becomes the question of negation - of the state. The state here refers both to the philosophical state-of-affiars, and to the political State. Both, similarly, obfuscate the process oh which they are built, as A state (this One and not an-other). Negating the state is changing it. Hence, by way of philosophy, Hegel, as THE philosopher of negativity, was and still is hailed as a proponent of critical and radical politics. Frantz Fanon used Hegel's master/slave dialectics to describe race-domination (1952), and Marx already used Hegel to articulate his critique of political economy (1867). Today, we are witnessing a revival in speculative thought, termed 'the speculative turn'. Besides, a more specific Hegelian-based rehabilitation of the idea of Communism is growing stronger with thinkers such as Badiou and Zizek.
Against these multiple non-analytical approaches, analytic philosophy is still very much dominant, especially among the richest parts of the world. This is by no means accidental. It bears witness to the very politics that is facilitated by such a philosophy. By such I mean the one that focuses on the positivity (what is in reality) and ignoring the negativity (what is not). This distinction results in reduction of truth to logical propositions devoid of any subjectivity, which after all, is the thing created and celebrated in its collective polity. By focusing solely on what exists in the world, and conceiving truth as a logical proposition (rather than a process of creation), analytical philosophers tend to focus on such related issues: semantical rules, the logical structure of language, propositional clarity, etc. The result is reducing real philosophical problems into the method of studying their expressive or representational means; it is the confusion/conflation of the methodological and the ontological, how we study with what is there to study.
We could conclude by saying that the form of philosophy prescribes some extent of its content, which in turn re-produces the very form. So starting with the position that philosophy is such and such, leads the philosopher to focus on certain parts of reality and in certain means. This, in turn, paves way for the kind of intellectual intervention produced by the philosopher. And this is where usefulness comes in. If we believe that reality is incomplete and could be otherwise, we might be more critical towards the political situation we are in. This is why, usually, speculative or synthetical philosophies stood in the forefront of many political revolutionary movements. And on the other hand, philosophers from more analytical approaches find politics to be outside their domain of expertise and maybe even responsibility. By focusing on language and assuming that truth is inside language, the representative, the real world, the presented, is left aside from both theory and practice. Thus analytical philosophy would be less useful in understanding the political and social situation in which we live. But synthetic philosophers always look for what is missing, and could be complemented by rupturing language, extending it, and reaching the real that is beyond its symbolic radar. In political terms, this means finding ever new ways to regenerate the subject, individual or collective, by freeing it from the torturing grasp of certain symbolic categories, the same ones which for analytical philosophers are the site of truth.
As you stated in 1867 Marx published his works on Capital. A Historical Materialist approach to understanding society. He has not been proven wrong. Before you can analyse society let alone critic it there must be an agreement what is the function of a given society in any given epoch. What is the modus operandi of Capitalism, if we can agree on this we can see it's raison d'etre, then we can ask questions about its function and limitations.