Q. Is There a difference between the shofar of the right side of the head of the ram or the left side?

A. Afarkasta De’anya (116) quotes Maharil that the intention of the verse (Yishaya 27: 13) ”In that day that the great shofar shall be blown,” is that Hashem will blow with the right side shofar which is bigger than the left one. Therefore there could be a preference to the right side shofar since it hints and alludes to that desired meaning. (See also Nitey Gavriel – Rosh Hashana 44: 1)

Horav Shlomo Miller Shlit’a pointed out to the Mishna at the end of Kinnim (3: 5) Rav Yehoshua says while the korban is alive it possesses one sound, but when it is dead its sound is sevenfold… its two horns are made into two trumpets (or shofros – Bartenura et. al.) It would seem that they were used indistinctly.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a