I'm sure some more experienced members could give you some more technical advice, but here's my 2 cents. I would try to learn using your right hand on the right side and your left on the left side. Then as you get comfortable doing that and progress into doing multiple passes you can experiment and find out what works for you. I for one switch it up. My WTG pass is done as earlier stated. My XTG pass is also for the most part, but I do use my right hand on the left side of my chin and vice versa. The same goes for my neck on the ATG pass (which I rarely do), I use the opposite hand because it feels more natural. Basically you are putting a very sharp object next to your face, by all means do what feels natural!

Actually now that I think about it I use the opposite hand for pretty much my whole ATG pass. For what it's worth.