"Eduard Hanslick, a firm friend of Brahms, could only speak with reserve of the composer's technical ability as a pianist whatever his admiration for the concert itself... and remarking that Brahms now had more important things to do than practise a few hours a day, a kind excuse for any technical imperfections there might have been in his playing."
Enough said.
By 1884 Brahms was definitely not concentrating on performing, and it was about this time he gave up public performance. However, as a young man, he partially supported himself with his performing and was good enough to get decent notices. Clara Schumann gave him a lot of instruction shortly after they met, and it apparently helped his tone production. He apparently had an incredible natural facility at the keyboard but was not the most subtle of pianists (and Clara was). And no, he was no Liszt...but he and the Schumann's were proud of the fact that they weren't, as they thought of Liszt as a showman and a superficial composer who was taking music in the wrong direction, pandering to the basest tastes.
In his late teens, to help his father make ends meet, Brahms took work playing piano in the singing halls that dotted the waterfront in Hamburg. These were places where a sailor could get a drink, watch a show, and enjoy some female companionship of a more intimate nature. Brahms, who played the popular music of the day by ear, was accompanist and provider of background music. One story is that he read Heine while playing -- had the book open on the music stand and read while he played, to elevate his thought while playing in those base surroundings.
He spoke bitterly of this early experience playing in these houses of prostitution till the end of his life. It wasn't easy work, the hours were terrible, he was a very pretty young man, and apparently the whores and sailors teased him mercilessly at times (the teasing was overtly sexual). For some boys, adolescent hormones raging, that environment might be a blast, but not Brahms, who was very sensitive and conscious of his higher calling at this young age. It was partly these adolescent sexual experiences that confirmed in his mind that women came in two types: whores and madonnas. It was a prevailing view men had of women at the time in Germany, just accentuated by Brahms's early experiences. For the rest of Brahms life, he idolized and worshipped some women (like Clara Schumann), thought of them as muses, inspirations -- but not as sexual creatures. He frequented prostitutes for his sexual needs, and what scant evidence we have indicates he treated them very well.
So Brahms had great facility at the piano, and he was frequently engaged to play concerti (e.g., Beethoven's "Emperor" was a staple of his repertoire). His facility was so good, the story goes, that he played the "Emperor" on a piano that was a half-step out of tune and transposed the entire piece up a half-step to be in tune with the orchestra. As Brahms matured and started making money from his composing, teaching, and conducting, he slowly discontinued public playing.
For me personally there is no contest between Brahms and Liszt as composers. Liszt was sometimes a better composer than some give him credit, but so much of what he composed was fluff designed to show off his technique and make his mostly female audiences swoon. That's why the emotions in Liszt tend toward the obvious. Brahms purposely modeled himself on the giant composers of the past -- Bach, Mozart, Beethoven, Schubert, Schumann. He was especially interested in retaining the classical forms -- which made him vulnerable to criticism from the Liszt/Wagner camp that he was stuffy and old fashioned. He thought of himself as continuing a tradition of composition where form, counterpoint, harmony, etc. were essential. Liszt and Wagner thought they were composing the music of the future, and it essentially abandoned the old forms, paid little heed to counterpoint, and devoted itself to creating emotional states in the listener. I can appreciate this type of music (Bruckner was the symphonist of the group), but it doesn't interest me nearly as much as music that contains form, structure, counterpoint, etc.
Sorry for the long-winded reply!
Topic: Brahms and Liszt