These days when we talk about the 'divide between analytic and continental,' we tend to see it through the lens of Carnap vs Heidegger (or Frege vs Husserl). With the flowering of analytic metaphysics, there is renewed interest in the Russell-Bradley dispute, so much so that among friends of Monism and the Principle of Sufficient Reason it is becoming a trope to consider that analytic philosophy was conceived in sin. But we forget a bit too easily that among Russell's principle targets we find naturalistic, Darwinian ethics and Bergson.
Now the main problem with naturalistic ethics as practiced by Darwinians (and others) is that it ties philosophy too closely to the present content (or "results") of (fallible) science. Russell correctly discerns that doing so binds philosophy to positions that constantly run the risk of becoming outdated. This is why Russell opted for modeling scientific philosophy on the durable methods of science (and confined ethics to non-philosophy). Interestingly enough Russell lumps Bergson with the Pragmatists (and here). In fact, it is Bergson who is treated as the antithesis of the analytic philosopher: he is the paradigmatic "synthetic philosopher."
Russell's main objection to Bergson was that he saw in Bergson an "anti-intellectual philosophy." Much of the details of Russell's argument against Bergson turns on their varying responses to Zeno's paradox and the status of mathematics. This is not the place to investigate the details (but it is worth noting that the birth of Analytic metaphysics can be traced to Jose Bernadete's critical appraisal of Russell on this score.)
Now, Russell is entirely correct to see in Bergson a pragmatist philosophy of science. For, on Bergson's account all enterprises that are symbolic or oriented around measurement (and that adopt ready-made concepts) are essentially action oriented. But as Russell surely recognized, Bergson's aspirations for philosophy (or metaphysics) are entirely different. Bergson introduced intuition precisely as a non-conceptual faculty that is oriented toward truth (and not action). (So, Bergson avoids Russell's criticism of the Darwinians.) Interestingly enough, such intuition is presupposed by scientific legislators (my term not Bergson's) when genuinely new (and profound) conceptual frameworks are introduced into the sciences. In fact, Newton's treatment of fluxions is the paradigmatic exemplar of this. But for Bergson in the progress of science the original insight often gets covered over by conceptual domestication that is a necessary consequence of science as puzzle-solving in the service of command and control.
Because of its non-conceptual nature, Bergsonian intuition is easily read in mystical fashion (and when one does so we easily fall into the dialectic between sober Analyticals and poetic/irrational Heideggerians). But intuition is just a species of sympathy (in the sense of Adam Smith). In particular, by "intuition is meant the kind of intellectual sympathy by which one places oneself within an object in order to coincide with what is unique in it and consequently inexpressible." The inexpressible need not be mystical. Sympathetic identification can be an affective state with content. (Cf. Deleuze on Spinoza, Hume, Bergson, etc.) In particular, such identification with multiplicity may well be presupposed by the scientific legislator when she coins new concepts that make a new future possible. Either way, by embracing intellectual sympathy, Bergson is merely following in the footsteps of that sober Scotsman, Adam Smith.
This is not the place to explore how to make further sense of this. Like Carnap on Heidegger, Russell writes as if he does not understand Bergson (for he never connects intuition with sympathetic identification, and prefers to tie Bergsonian intuition to Hegelian "errors") and pretends to do battle on the level of technicality.
Even so, Russell offers the briefest of hints that he does understand fully what is at stake in commenting on Bergson; he writes from the perspective of "a cool critic, who feels himself a mere spectator, perhaps an unsympathetic spectator..." That is to say, in the process of birthing analytical philosophy, Russell cannot allow himself to feel sympathetic identification with the Bergsonian project, while simultaneously criticizing it; for then he -- the great logician -- would be caught in a performative contradiction. Even so, Russell ends his majestic History of Western Philosophy (a book that skips Adam Smith) with an ode to sympathy, of course.