Always an ensemble to do things differently, the Budapest Festival Orchestra has turned itself into a part-time choir. We discovered this at encore time. "We perform for you Johannes Brahms's Abendständchen," conductor Iván Fischer announced, after the BFO had played the composer's Third and Fourth symphonies. Clutching scores, the musicians hastily regrouped themselves on the platform.

Abendständchen is one of Brahms's most beguiling works for unaccompanied chorus, and the orchestra sang it with remarkable precision and finesse.

Fischer's approach to Brahms's symphonies, however, isn't to everyone's taste, and the main programme was a more ambiguous affair. The playing was extraordinarily beautiful, but some would no doubt question the conductor's deployment of substantial forces – a big body of strings, in particular – and his fondness for a plush, almost post-romantic orchestral sound. Beauty isn't everything in Brahms. Opulence sits uneasily with a composer frequently associated with leanness and rigour, and tends to obscure the sinew and muscle beneath the music's flesh.

The two symphonies are often seen as a contrasting pair: we tend to describe the Third in terms of intimacy, and the Fourth as epic or tragic. Both, however, are haunted by intimations of mortality, and Fischer finds sadness as a dominant emotion in each. We hear it in the drooping lyricism of the opening movement of the Third, and in those moments in the Andante and Scherzo of the Fourth, in which the music's confidence seems briefly undermined by bewilderment. But in this instance, the insight came at the price of momentum, above all in the Third, which didn't fully exert its grip until we reached the last movement. Fischer's performance of the Fourth was all about subtle gradations of tension rather than raw intensity, and there were moments of great power, in the climactic Passacaglia above all.

• The Proms continue until 13 September. Details: Proms 2014.