The accounts of Carl Halir’s playing that I’ve read are varied, and haven’t come together yet to form a clear picture. I was therefore interested to read Theodore Spiering’s column in The Musician on the occasion of Halir’s death in 1909. Spiering (1871-1925) studied with Joachim at the Hochschule around 1890, and took part in a few Joachim Quartet performances. He returned to the US and began his illustrious career by joining the newly formed Chicago Symphony Orchestra from 1892-96.
Here Spiering compares Halir as a member of the Joachim Quartet to his predecessor, Heinrich de Ahna, and recalls his performance of Spohr’s “Gesangscene” Concerto No. 9 and the Beethoven Concerto during his American tour of 1896-97. The scan of the article is not easy to read, so here are some quotations:
On Halir as a quartet member. “Though he was a greater soloist than de Ahna had been, he did not quite fill his predecessor’s place to my entire satisfaction. Possibly owing to the fact that he was accustomed to leading his own quartet at the same time that he was a member of the Joachim Quartet, it seemed that he was not quite in sympathy with his task.” (This seems to be logical assertion, but goes against the numerous accounts of the Joachim Quartet’s famed unity, responsive to the slightest indication from their unpredictable leader.)

On Halir’s interpretation of Spohr and Beethoven. “I will never forget the impression he created with his performance of the [Spohr]. It was perfection of style, technic, and beauty of tone combined: in short, it was such a noble performance and so satisfying in every way, that it will ever be a delightful remembrance. The Beethoven, unfortunately following this splendid achievement, fell somewhat short in lacking, to a certain degree, the bigness of conception that I had been won’t to expect from Joachim’s teaching and playing.”

The Musician (1910): 199.

Halir also played the Beethoven and the Spohr on his New York Philharmonic concerts, and there is another review of him playing these two concertos in Vevey, Switzerland, in 1903.

Halir seems to have had an insatiable appetite for playing, which made it possible for him to maintain at the same time a solo career, multiple chamber ensembles and leading an orchestra. He also seems to have had no technical difficulties: not only did he have both the Brahms and the Tchaikovsky Concertos in his repertoire, he played them both on the same concert! The Berliner Tageblatt proclaimed that with that performance, “he has won a place among the most important violinists of the day. The qualities that distinguish his playing are a powerful tone full of grandiosity; great technique paired with utter security; and a fiery, musically formed, and noble performance.” 1H.E., Berliner Tageblatt, 28 January 1888.