If I can add a tangible reason for the difference (other than the obvious one - who has the better mods???) then remember to consider that there are two ways in which auto battle can be used on offense. With and without targeting.
By default on offense, when you click auto the AI will use targeting and all attacks will be directed at 1 character. This targeting will priorities 1st the character that was selected when auto battle is clicked (which is the leader when you enter battle and don't select someone else) then once the targeted character is defeated targeting will proceed to leader -> front row left -> front row right -> back row right -> back row left. This progression is disrupted by taunting tanks but will resume once the tank is defeated, targeting will not switch from the tank until it is defeated however whether it is taunting or not.
If you click the targeted character, while on auto, targeting will be disabled and the offense AI will use the same heuristics as the defense AI to select targets. Non-targeted AI initially chooses target randomly (apart from characters with specific targeting such as the Revan brothers). Once with each subsequent attack there is a probability (unknown to me but ~20 to 30% in my experience) that the target will randomly change to another random enemy.
When using auto it's normally advisable to use targeted auto battle but be careful to select yourself the best character to target. If you don't choose wisely which character to target then the defense AI with it's untargeted attacking could very easily have the advantage. If you deselect the target while using auto you will have a more fair comparison (but always the slight advantage as you have to choose who your first target is when you turn on auto battle).
In addition, abilities that target characters on your own team will use heuristics such as "lowest combined health and protection" or other metrics to determine which character to target. If you are modded or geared differently to the opposition team these abilities will be used differently. It is in your control how you use this to your advantage / disadvantage.
Finally, can I suggest you and your opponent switch to palp lead? It's much better than Dooku's when running sith ;)
Best of luck!