I like the Kleiber performance, too, but yes, it is slightly more controversial. Amazingly, Kleiber manages to find a more authentic 'Viennese' sounding Schubert within this score, despite the obvious Haydn influence, if that makes sense? as he seems to consciously resist focusing on the more Haydn-like aspects of this symphony, but instead is able to find & bring out the elements of Schubert's own distinctive, emerging voice--even though it wasn't yet fully formed, IMO (see my comments below).
Here are some other fine Schubert 3rd recordings that I've liked over the years, if you're interested in doing some selective, comparative listening--in order to get a better sense of where exactly Kleiber's Vienna performance stands, interpretatively, within a crowded field of recommendable recordings:
I. On modern instruments (i.e., the older, more traditional interpretations),
--Wolfgang Sawallisch, Staatskapelle Dresden, Philips--an analogue recording from the 1960s--for me, this performance has its own unique musical insights, although some may find it too old fashioned & overly slow in places. (IMO, Sawallisch's time in Dresden produced some of the finest recordings of his career: the period included a very good Schubert 1-9 cycle, & one of the top cycles of Robert Schumann's 4 Symphonies, as well as Sawallisch's earliest, superb recordings of three of Schubert's best known masses).
--Herbert Blomstedt, Staatskapelle Dresden, issed by both Berlin Classics & Brilliant--an analogue recording from the 1970s. Here is the great Staatskapelle Dresden (in those days) recorded a decade or so later in slightly better analogue sound than under Sawallisch. For me, both Sawallisch & Blomstedt are more insightful Schubertians than Abbado.
--Sir Thomas Beecham, Royal Philharmonic Orchestra, from 1958-59. In my view, this is the best of the pre-stereo era recordings of Schubert's 3rd symphony--at least I believe it's late mono (but very good mono), & a stylish, strongly characterized performance:
--Otmar Suitner, Berlin Staatskapelle, Denon--Suitner's set is currently my digital cycle of choice among the 'old school' accounts (it was recorded in 1988); since I can find Sir Colin Davis's Dresden cycle to be hit & miss; though admittedly Sir Colin was perhaps at his best in Schubert's earlier, more "Haydn-esque" (or Mozartian) symphonies (& the 8th), such as the third, seeing that he was a Haydn conductor of the first rank. So you may wish to compare the Suitner & Davis digital 3rds (see my links below).
Though personally, I can't tell much, if any difference between Davis's style of conducting in Haydn & his Schubert 3rd myself--as it sounds exactly like his Haydn, style-wise, & I'm not sure that's entirely a good thing?, especially after you've heard some of the period & HIP performances... such as Immerseel's, for example (see below). Nevertheless, the Staatskpelle Dresden does play fantastically well here, as usual (in superb digital sound), & it's a very fine performance:
Suitner:
Davis:
Eugen Jochum was another great Schubert conductor, but I don't believe he ever recorded the 3rd. Nor did Pablo Casals, either. You might also want to check out Istvan Kertesz's Schubert, too, since he likewise had a good reputation in this music.
II. HIP, on modern instruments (all digital recordings),
1. Nikolaus Harnoncourt, Royal Concertgebouw Orchestra--speaking of hit & miss conductors, here Harnoncourt dusts off the cobwebs with his extensive experience in the period movement, & turns in a riveting HIP performance of the 3rd that is extremely well played by the Concertgebouw musicians--definitely one of my top 3 or 4 picks, overall:
Symphony No. 3 in D Major, D. 200: I. Adagio maestoso - Allegro con brio
Symphony No. 3 in D Major, D. 200: II. Allegretto
Symphony No. 3 in D Major, D. 200: III. Menuetto. Vivace - Trio
Symphony No. 3 in D Major, D. 200: IV. Presto vivace
2. Antonello Manacorda, Kammerakademie Potsdam, Sony:
https://open.spotify.com/album/2NimhoIUkYOPTbTKkKMTAx
3. David Zinman, Tonhalle-Orchester Zürich:
Symphony No. 3 in D Major, D.200: I. Adagio maestoso - Allegro con brio
III. On period instruments,
--Jos Van Immerseel, Anima Eterna Bruges, Zig-Zag territories--from a complete 1-9 cycle. What separates Immerseel's Schubert from other cycles is that he took the pains to find authentic Viennese horns from Schubert's own time, and the different orchestral balances that creates can be fascinating to hear. With the result being that you tend to notice the horns more, which is a good thing, IMO, because it makes the symphony sound a lot more like Schubert was under the spell of Beethoven, in places, rather than just Haydn. Which appropriately puts the symphony into a later context, where I think it belongs. Hence, this is one of my most essential top picks for the 3rd:
Sinfonie No. 3 in D Major, D. 200: I. Adagio maestoso - Allegro con brio
--Frans Bruggen, Orchestra of the 18th Century, Philips--another terrific period cycle & 3rd. I can never decide which cycle I prefer between Bruggen & Immerseel's. Both are excellent. Though Bruggen does have the more extensive experience conducting Haydn Symphonies, if that matters here (though, to be honest, I've never actually sat down and compared their 3rds).
Schubert: Symphony No. 3 in D Major, D.200 - 1. Adagio maestoso - Allegro con brio
Bruno Weil is another period conductor who is very fine in Schubert, however, I don't believe he has recorded the 3rd.
I've not heard Marc Minkowski's Schubert.
With that said, as mentioned, I don't think Schubert had quite fully found his voice as a symphonic composer by the time of the 3rd, & wouldn't do so until his 4th & 5th Symphonies (both of which I prefer to his 3rd). To my ears, Schubert's first three symphonies tend to be more heavily under the influence of Haydn & Mozart, & at times Beethoven. Which doesn't make them bad or any less enjoyable, but I don't think of them as being fully mature Schubert yet. So, perhaps the 3rd benefits from what Kleiber does to it?