Brahms's piano concertos are two of the greatest pillars of the Romantic repertoire. The first, written in 1858 when the composer was still a young man, is like a symphony where piano and orchestra seem involved at times in a titanic struggle, themes are hurled across the stage with dramatic rhetoric; the second, composed two decades later, feels more like a massive chamber work, where the musical ideas are an exchange rather than a confrontation. If the first is more about proclamation, the second is perhaps more about reception - a speaker versus a listener. The way each piece opens tells this story in a few seconds: the first with its ferocious drum roll, a clap of D minor thunder pinning the audience back in its seats; the second with a gentle horn solo inviting that same audience to learn forward in dialogue.

GK Chesterton, in a typical bon mot, wrote: "Bleak House is not certainly Dickens's best book; but perhaps it is his best novel." If I could borrow and paraphrase that, I might say that of the two Brahms piano concertos the second is the better piece, but the first is the greater. I think the second is better constructed, better orchestrated, themes are better developed, harmonies are better judged, textures are better balanced - but for me the earlier work has a greater burst of pure, utter, natural genius. Its flame flares with such intensity, and with such promise of more to come (he was only 25 years old when he wrote it), that I find myself overwhelmed by it in a way I'm not by his second (and final) piano concerto, written 22 years later.

That is, until I recorded and played them both in the same concert in Salzburg last year. The first concerto is work enough for one evening (or morning on this particular occasion) but when the interval arrived, instead of the usual backstage process of winding-down, I had to crank up for an even bigger piece and challenge. Returning to the piano on the Grosse Festspielhaus's stage, I was physically warmed up but emotionally spent and drained, sated by the richness of the first half's feast. But then the horn solo sang from the back of the stage and I replied with that gentle, lapping, ascending arpeggio (has a more intimate moment of chamber music even been woven into a piano concerto?) and instantly I was refreshed by this most conciliatory of musical exchanges, Brahms at the height of his confident maturity. As the orchestra took over from me after my first cadenza with their ringing B flat major tutti (only one forte not two) I was completely revitalised, as if I had received a shot in the arm - music's second wind, the eagle's strength-renewed wings.

Doing the Brahms double ... Stephen Hough. Photograph: Sim Canetty-Clarke

Brahms's final stroke of genius, after the ravishing slow movement where lyrical song-like sections frame a turbulent central climax more anxious than tragic, is the Allegretto grazioso finale. Many have suggested that this understated, joyful movement lets the work down and is a misjudged anticlimax. I personally think the only misjudgment is when performers ignore Brahms's flowing metronome marking in the Andante and create a heavy-handed movement which makes the work's overall structure lopsided. The graceful last movement, from its opening when the melody shyly sidles in on the subdominant through its later à la hongroise moments to the finale Tarantella, is one of Brahms's greatest compositional triumphs.

For all the grandeur and excitement of the first concerto's youthful flare, the second's older vintage seemed wiser, more fascinatingly complex as I revisited and re-recorded both pieces last year. Its musical arguments seemed more nuanced, more open to exploration, more a search for common ground where, as in life, the sun can shine brightest ... and warmest.

• Stephen Hough's recording of Brahms's Piano concertos is out now on Hyperion (read our review). He performs Lizst's First Piano Concerto in Sheffield on 14 February and Manchester on 15 February with the BBC Philharmonic Orchestra.