I was told, the reason the 2nd side hurts more, is because as soon as the first side is started, all the little pain-killing endorphins rush to that side...then you start the 2nd side, but there are less endorphins to go to that side to kill the pain!
With regards to the right/left side debate...I was also told that your dominant side has more hair on it than the other side. It's really easy to see on bikini lines/underarms/eyebrows, and I've found that it's usually true.
So, if you are right-handed, and therefore, the right side if your bikini line has more hair, you're best to start waxing this side. Then, when you get to the left side, although there are no endorphins left, there's less hair so it should be slightly more bearable than if you'd done it the other way round.
Still hurts though!