I shouldn't be recommending recordings of the Brahms String Quartets, since I prefer his other chamber works--such as the 2 String Quintets, 3 Violin Sonatas, 2 Sextets, Piano Quintet, Clarinet Quintet, 3 Piano Quartets, etc., and even in concert I've found my mind wandering during parts of his SQs...
So, for Schumann's String Quartets, I'd recommend looking into and sampling from the following recordings, which I've listed in two groupings (or rather three, if you're interested in historical recordings):
1. Here are the recent recordings--HIP, period, & otherwise--that I've most liked (& *=performances that I thought were extra special):
--*Quatour Hermes:
a super fine, young quartet, who are thoroughly attuned to these quartets. It also sounds like they've considered the music from the standpoint of period practice in the 1830s. Strongly recommended.
--*Quatour Terpsycordes (on period instruments)--I slightly prefer Terpsycordes to the Eroica Quartet, who similarly play on period instruments and offer more romantic performances that are probably easier to 'like' initially than those by Terpsychordes:
. I should mention that this group went back to Schumann's manuscripts of the first two quartets and found that some of the peculiarities in his original notations--which he had conceived pianistically--had been smoothed over by later performers and editors, causing Terpsychordes to question the published scores. (Note that the group had already been playing the 3rd quartet in their repertory for years.) So, these performances are more authentic to 1830s period practice & to Schumann's original thoughts than most, and I'd recommend them. (By the way, Terpsychordes was the first quartet to record Beethoven's magnificent Op. 132 String Quartet on period instruments, and it's a 'must hear' performance, IMO:
.)
--*Zehetmair Quartet--SQs 1 & 3: This recording impressively won both the 2003 year end Gramophone chamber music award, and the Gramophone 2003 "Recording of the Year". It was also recently recommended by the BBC Radio "Building a Library" segment in January of 2019. I find the performances excellent and challenging at the same time: Gramophone wrote,
"The Zehetmair Quartet coupling focuses the music's alternating wildness and fragility with altogether unique perception. Theirs is an agitated, combustible and loving view of Schumann..."
Here's the rest of the article:
https://www.gramophone.co.uk/review/schumann-string-quartet-nos-1-and-3
--Eroica Quartet (on period instruments): These period recordings are excellent, too, and could easily be a first recommendation for some listeners:
Here's what critic Edith Eisler had to say about the Eroica Quartet's Schumann:
"Though the members of the Eroica Quartet, formed in 1993, belong to various period-instrument groups in their native England, they have developed their own brand of performance practice: they play on gut strings, with sparing vibrato, but at normal pitch; the cellist uses an end-pin; the others use chin rests and shoulder pads. Moreover, instead of researching manuscripts and ur-texts, they consult early editions prepared by musicians active during the composers' lifetime, such as Mendelssohn's friend and adviser, the violinist Ferdinand David. Using his bowings and fingerings may give their performances "authenticity," but it is questionable whether the resulting innumerable slides and accents, which we have since learned how to avoid, are not ultimately to the detriment of the music. The Quartet is good; its taking over and interlacing of voices is excellent, its intonation almost perfect. The playing is warmly romantic and both lyrical and dramatic, but the accents are too aggressive, the liberties too planned. The Scherzos are sometimes a bit heavy, perhaps to avoid sounding Mendelssohnian. The popular third quartet is unusually inward at the expense of its rapturous ecstasy. The cellist struggles with his high register, the Finale is rough and quite unrhythmical, the problematic transitions between the sections lack poise and smoothness. The second, least familiar quartet comes off best: it is elegantly phrased and gracious, and the all-pervasive syncopation is handled very well."
https://www.amazon.com/Schumann-Str...chumann&qid=1556184875&s=music&sr=1-1-catcorr
2. Among the more traditional SQ ensembles, who tend to be smoother & more lush with added tonal heft compared to what is heard on the period & HIP Schumann performances (with the exception of the Gewandhaus Quartett, who play in a tradition that goes back to Schumann & Mendelssohn's time), I'd recommend the following:
--*Gewandhaus Quartet: a later incarnation of the group that originally premiered Schumann's Op. 41, No. 3 quartet in 1838--they play with impeccable intonation and blending, & are heard in superb Hybrid SACD sound. Strongly recommended:
https://www.amazon.com/Mendelssohn-...+schumann&qid=1556181151&s=music&sr=1-1-spell
The one negative is that you have to buy three CDs in order to get all of their Schumann recordings; however, the Mendelssohn SQ couplings are first rate, too, and very recommendable (although their Mendelssohn SQs were issued as a complete set by NCA, unlike their Schumann):
https://www.amazon.com/String-Quart...+schumann&qid=1556181151&s=music&sr=1-2-spell
https://www.amazon.com/Mendelssohn-...+schumann&qid=1556181151&s=music&sr=1-1-spell
--*Cherubini Quartet: excellent playing, in superb sound, at least on the EMI Classics "Double fforte" 2 CD discount reissue that I own (as I've not heard the more recent Warner reissue):
https://www.amazon.com/Schumann-Pia...chumann&qid=1556182361&s=music&sr=1-2-catcorr
--*Ysaÿe Quartet: more very fine performances, with extra tonal heft, in superb sound:
--Leipzig String Quartet--Op. 41, and Piano Quintet (with pianist Christian Zacharias): I agree with the following review:
http://www.classical-music.com/review/schumann-piano-quintet-string-quartets
--Hagen String Quartet: I tend to have mixed feelings about the Hagen's Schumann, as some movements are played to perfection, while I prefer other groups in certain other movements: For example, I find the following performance rather suave & impersonal compared to other ensembles that, IMO, find a more fragile pathos in the movement, such as Quatour Hermes & the Zehetmair Quartet, etc.:
. And yet, the Hagen's playing of the Adagio here is exceptional:
--Melos Stuttgart Quartet: very good, solid performances in excellent digital DG sound, which offer the attraction of 'one stop shopping', as the 1986-87 DG box set includes both the complete Schumann and Brahms SQs (most recently, the set's been reissued by the Newton label):
https://www.amazon.com/Schumann-Bra...bel+melos&qid=1556179873&s=music&sr=1-1-fkmr0
https://www.amazon.com/Robert-Schum.../dp/B00000E40N/ref=cm_cr_dp_d_rvw_txt?ie=UTF8
I've not heard the Takacs Quartet in Schumann, but I expect they're exceptional. Nor have I heard the recent recording from the Elias Quartet, or the Auryn Quartet on Tacet (a label known for its audiophile sound quality), the Alexander SQ, the Fine Arts Quartet on Naxos (though I wasn't overly keen on this group's Mozart), the Doric Quartet (whose Schumann gets glowing reviews), the Lark Quartet, or St. Lawrence Quartet, either--all of whom have received excellent reviews.
I'd also keep an eye out for any future recordings from the Tetzlaff Quartett in this repertory, as their 1st violinist Christian Tetzlaff has a special affinity for Schumann's music. (The same is true for violinist Ulf Wallin, but as far as I know, Wallin doesn't play in a string quartet...) I'm also expecting the Dover SQ to record Schumann in the future, as they've played this music in concert, as has the excellent Quatour Ebene:
Goodness, there used to be such a dearth of recordings of Schumann's String Quartets! I can remember when the Alberni SQ on CRD was basically your only option on LP, but that has drastically changed, now there's a glut. I'm not complaining... especially since Schumann considered his 3rd String Quartet to be one of his finest works, so it certainly deserves many recordings.
--Historical recordings--In general, I'm not entirely enamored with the historical Schuman SQ recordings, finding the heavy violin slides out of place in early romantic music, along with the often glaring intonation lapses, and of course the poor recorded sound, but will admit that these groups have their followings:
Capet String Quartet:
Flonzaley String Quartet:
Léner Quartet:
Prague Quartet...
With the exception of Quartetto Italiano, who are excellent, as usual:
1950:
1959:
Finally, I'd be remiss not to mention that Schumann's amazing Piano Quintet, Op. 44, and Piano Quartet, Op. 47--both in E-flat major--are even more essential among his chamber works, in my opinion.
My 2 cents.