Are there certain symmetric-pair muscles that are slightly bigger and NOT due to handedness?
There are many variables that could affect the answer to this question. Such as what activities you partake in. 

For example, I am a hockey player at the he varsity level in high school. I have noticed that my entire right side is more toned, muscular, and flexible (especially my right latisimus dorsi and deltoid). It just so happens that I rely on my right side for energy and strength more than my left when it comes to shooting pucks and just playing the game.

Typically what we see in humans is the dominant side of their body will tend to show more hypertrophy than the non-dominant side. When you look at a human anatomically, their dominant side shoulder will be bigger and will rest lower when relaxed. Even small things like sleeping habits can effect the visual difference of you symmetry. I will agree though that it is odd that your friend noticeably has more hypertrophy in his neck muscles on one side but is dominant on the other side. This could be due (but not limited) to small habits not taken into account. Like I mentioned before, sleep habits, any motion with the neck in a specific way, chewing could maybe be a factor, or (maybe not likely) a genetic mutation.

This is an interesting topic and I urge you to maybe look at some more people for evidence that dominance has a role in it. 2 people is maybe not enough evidence to really back up a claim you're going to make.

Hope this helped!

-Sartoaster