He was reputed to be able to produce a beautiful tone, with exceptional mastery of the low register of the basset clarinet and distinctive basset horn playing. A contemporaraneous Viennese critic, referring to Stadler, wrote, “I would not have thought that a clarinet could imitate the human voice so deceptively as you imitate it. Your instrument is so soft, so delicate in tone that no-one who has a heart can resist it." A noted virtuoso, he played second clarinet to his younger brother Johann Nepomuk Stadler (1755–1804) in the Vienna Court Orchestra. It was possibly this specialism in second clarinet along with the basset horn that led to his collaboration with Theodor Lotz (1746–1792), a clarinet maker. His idea was to add an extension to his B-flat and A clarinets – in the same vein as the basset horn – an extra major third to a low C. It was for this extended clarinet (now known as the basset clarinet but initially called a bass clarinet in the days before the modern bass had been invented) that the Clarinet Concerto and possibly the Quintet for Clarinet and Strings were written. A concerto in D major for basset clarinet was written for Stadler by Franz Xaver Süssmayr, which remains as two incomplete manuscripts. It is now thought that the clarinet concerti by Joseph Leopold Eybler and Leopold Kozeluch were also written for Anton Stadler.
Owing to financial problems during the 1790s Stadler, who in 1796 lost his job in the court orchestra, toured northern Europe performing concerts on the basset horn. Shortly after 1800 he left his wife and family and moved to the Landstraße where he lived with his mistress, a certain Friederika Kebel. He died of emaciation and was buried on 17 June 1812 on the old Catholic cemetery in Matzleinsdorf. Contrary to widespread information in the literature (Albert R. Rice, Poulin, Zaslaw et al.) Stadler's son Anton was not a basset horn player. He played the "Passetl", which in Vienna describes a small stringed bass.
Stadler's compositions included "Terzetten", eighteen short pieces for basset-horn trio.