The photo I’ve put at the head of this blog was taken at one of the Paris conferences (1936 or 1937). A couple of years later, Russell came to the University of Chicago for a quarter (perhaps two — long enough anyway for the U of C to count him as one of their faculty awarded a Nobel Prize); Carnap and Russell had the opportunity of weekly confrontation in a regular seminar. The scene is described vividly by Abraham Kaplan, a postdoc there at the time, and later a colleague of Carnap’s at UCLA, in a memoir published as part of Ed Shils’s Remembering the University of Chicago: Teachers, Scientists, and Scholars (1991), a great collection on a once (and perhaps still) great university:
The contrast between the styles of the two philosophers was even more exciting and instructive than the content of the seminar. Russell wielded a rapier — thrust, cut, and parry, with flashing wit and insight. Carnap was a whole panzer division all by himself, a Star Wars fighting machine clanking inexorably with heavy tread and crushing all in its path. (p. 40)
The whole memoir is worth reading, if only to see how venerated Carnap could be by a philosopher who was really on a completely different wavelength. One begins to see why, despite this, it was in response to Kaplan that Carnap decided to set out his conception of values more systematically (last chapter of the Schilpp volume).
The actual substance of the philosophical tensions between Carnap and Russell — as opposed to the difference in style — is more elusive, but Chris Pincock in the Cambridge Companion to Carnap makes a very good beginning. It’s an interesting case; Carnap probably identified more with Russell than with any other living philosopher, but differed from him quite fundamentally in philosophical doctrine. In retrospect, Carnap is — correctly, I would say — seen as closer to the neo-Kantian tradition and to Frege than to Russell and British empiricism, but he himself would not have been very happy with that.