Happy walks on my right side and passed his CGC that way. The evaluator asked which side I preferred and that is the way that I taught him. I have issues with my left shoulder so didn't want to walk him on that side- he pulled before I got his Gentle Leader. Callie walks on the left- she came that way- great loose-leash walking and she passed her CGC walking on my left.
For obedience competition and rally competition, the dog should be on your left. For agility, they need to be able to go to either side. so how you walk 2 dogs depends on what you want to do. For exercise, doesn't matter. For competing, it will matter.