Good question! Euler and Gauss are widely recognized as being the 2 most influential mathematicians in history. The greatest contrast between these 2 is that Euler worked on anything and everything, and published A LOT. In contrast, Gauss was more of a quality over quantity type of guy. He kept to a few topics and spent a lot of time improving his theorems and proofs before publishing anything.
Wikipedia on Euler:
Euler worked in almost all areas of mathematics, such as geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics. He is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 quarto volumes. Euler's name is associated with a large number of topics.
Carl Gauss was an ardent perfectionist and a hard worker. He was never a prolific writer, refusing to publish work which he did not consider complete and above criticism. This was in keeping with his personal motto pauca sed matura ("few, but ripe").
So yeah this is probably why the "mirrored" Sodachi prefers Gauss over Euler.