The dominate side is usually a bit larger and strong than the other side. Right handed people suggest a stronger and larger right side. Left handed, the opposite. Even the Pro's are stuck with this.
The dominate side will lead, as in the BB bench press for example. If having a hard time on the last rep, you may notice the left hand trying catch up to the right hand, if you are right handed. Might consider more focus on DB or single handled grip machine work, could help a bit. Good Luck.