I guess it depends on how much of a difference in strength you are talking about. My right arm is stronger than my left for sure. I train them with the same weight, but I sometimes can't complete the set on the left. LIke say I complete 12 reps on the right, sometimes I get to 10 on the left. If that is the difference, then I would still lift the heavy amount and just work the left arm to failure. That is what STS is all about. Pushing yourself to failure. (meaning, that you lift until you can't possibly finish another rep without losing good form.) However, if you can only lift that heavy weight 3 times on the left vs the 12 on the right side, then obviously you need to lower the weight for both arms. Definitely keep the wieight you use the same on both arms. I would not increase the weights until you can complete each set totally on both sides.
Hope this made sense!