Yeah, there would likely be some notable differences in speed. The larger a planetary body is, the more readily it can hold on to lighter elements, and the lower the average molecular mass will be. This would result in higher sound speeds and higher sound pitches at the same temperature as you move to planets of higher mass.
Mind you, this is a general trend. There are counter-examples in our own solar system: Venus and Mars both have atmospheres with a mean molecular weight of 43 g/mol, even though Venus is significantly more massive. But Venus is an odd duck in pretty much every way.
Then, of course, you have to take into consideration that less massive bodies can hold on to atmospheres with lower molecular weights the colder they are (planets lose the lighter elements due to them essentially boiling off into space; with less heat, there is less chance of losing those lighter elements). For this reason, Pluto has an atmosphere with a mean molecular weight comparable to that of Earth’s. But, of course, the speed of sound on Pluto would be very different compared to on Earth due to the extreme temperature difference.