The “Augsburg aurochs” made by Charles Hamilton Smith in 1826 is one of the most famous depictions of an aurochs. It is based on an oil painting which dates to the 16th century and that was purchased by Smith in Augsburg, Germany. The oil painting, which might have been based on a live aurochs, is now lost and there are no photographs of it. The only thing we have is Smith’s copy of the painting, the “Augsburg aurochs”. “Copy” is a bit misleading, as Smith probably did not track out the original work but made his own version of it. For example, the animal on the original painting had an “entirely sooty black” colour, except for a white chin , while Smith decided to paint his aurochs in brown for whatever reason. The black and white version of Smith’s artwork is widely publicised, but the original work is coloured and shows a brown animal as you see down below .
Wikipedia cites a source which itself cites two sources that the original that Smith’s artwork is based on might not show an aurochs at all: one source claiming the painting might have been based on a hybrid between aurochs and cattle, and another one claiming it might have been based on a Polish steer.
To see if there is anything legitimate behind these ideas, let’s have a look at Smith’s artwork. We do not know what the original looked like, except for the fact that the original bull was entirely black with a white chin. This is a colour that agrees with the other sources for the colour of the aurochs that we have, only the light dorsal stripe was apparently lacking on the original. This does not necessarily have to mean that the animal the painting was based on lacked a dorsal stripe, since this trait is not visible from every perspective.
The animal portrayed by Smith matches an aurochs very well in proportions. The trunk is short, the legs are long, the head is large. The horns have the curvature of an aurochs’ horns and face forwards, and also the size is aurochs-like. The ribcage is deep as in the aurochs, and the waist is slender, creating a triangular shape for the trunk, which was very likely a trait of the aurochs as all wild bovines have that kind of trunk. The head has curly hair on the forehead, which is a trait that is well-documented for the European aurochs . The head looks a bit paedomorphic with its concave snout and large eyes, but Smith tended to stylize his animal depictions. The dewlap is very short, as in the aurochs. The animal seems to have a woolly coat, and historic reports say that aurochs were covered in longer hair than domestic cattle , which is plausible for a wild animal living in temperate Europe. All in all, Smith’s depiction looks much like an aurochs, except for the wrong colour, which was aurochs-like in the original. It is most parsimonious to assume that the aurochs-like traits found in Smith’s work were also found in the original oil painting, otherwise it would be a big coincidence that Smith’s work happened to be more aurochs-like, in a time when we did not have a very good picture of the aurochs’ life appearance.
One could argue that the lack of a penis tuft is a hint that the original artwork was based on a domestic steer, as steers usually do not have one. Also, the neck bulge is not very prominent in Smith’s work (steers have none). However, we do not know what the original looked like. Perhaps Smith was not paying attention to these two traits when he did his artwork. Perhaps the artist of the original from the 16th century did not pay attention to them. Smith’s work, however, definitely shows a scrotum.
As for the arguments claiming it was a hybrid between an aurochs and a domestic animal, I don’t know what exactly lead the author to conclude that it was a hybrid as I do not have access to the work in which it is postulated. But I cannot derive any possible reasons that lead to this conclusion based on the artwork, because Smith’s aurochs actually looks much like an aurochs and a wild bovine (the morphology, the dynamic pose and the slender waist suggest a wild animal to me).
Also, the original painting had the word “Thur” written in golden letters on it , which is the Polish name of the aurochs. Back in this time, aurochs were only found in Poland  and also South-Eastern Europe (Moldavia). The usage of the word “Thur” suggests that the artist had seen an aurochs in Poland, where the last aurochs were found. In Poland, people strictly distinguished between the aurochs and the wisent, because both animals were still found in this country, and they knew what they looked and were like. I see no reason why this word would be used for a domestic steer.
All in all, I think it is highly likely that the original painting Smith’s “Augsburg aurochs” was based on showed an aurochs, that the original probably was a rather accurate depiction of an aurochs because Smith’s work is that too (except for the wrong colour), and that it is well probable that it was painted after a live aurochs. It seems that most authors assume it showed an aurochs, and I see no convincing, compelling reasons to assume otherwise.
 van Vuure: Retracing the aurochs – history, morphology and ecology of an extinct wild ox. 2005.
 Frisch: Der Auerochs – das europäische Rind. 2010.