James L. answered 07/01/20
Doctor of Musical Arts in Piano from Yale University, Faculty UCLA
I have always read in books and heard from colleagues that Brahms is regarded as more profound and mature, and has more depth than Rachmaninoff in general. In the case of the Brahms Concerto 2 versus Rachmaninoff Concerto 3, part of the reason is that Rachmaninoff was 36 when he wrote Concerto No. 3, and Brahms was 48 when he wrote Concerto No. 2. That may not seem like such a huge difference, but when you look at all the other works Brahms wrote leading to Concerto 2, you can see a similar journey in Rachmaninoff's life. Both were composers whose earlier works were more virtuosic, flashy, and melodically memorable; while later in life both composers tended to value harmony, structure, and a certain spiritual other-worldly quality that comes with more maturity.
One might say that Brahms matured faster than Rachmaninoff due to their differences in priorities in life- Rachmaninoff was more of a performing pianist whose composing was more to serve audiences. Brahms was also a pianist, but spent more time composing and perfecting his craft. It is also worth noting that compared with their other works, Rachmaninoff's Concerto No. 3 is more of a middle period work within his life, and for Brahms, Concerto 2 is more of a late period work created during his most mature years. Therefore, there is a consensus that one needs more maturity and depth to interpret the Brahms 2nd Concerto than the Rachmaninoff 3rd Concerto. Structurally, the Brahms is a bit more complex and requires both refinement and maturity, whereas younger pianists can relate to and perform Rachmaninoff's 3rd concerto more readily, as it still contains some of his youthful vigor. Both are certainly mature works, but I agree that Brahms 2nd Concerto is more mature than the Rachmaninoff 3rd Concerto.