As mentioned above, the Union army quickly tended to phase out mixed batteries. During Meade's large scale initial assaults at Petersburg, the batteries with rifled tubes were used to hit the city of Petersburg itself while the batteries with 12lb Napoleons targeted Beauregard's actually trench line for suppression.
In the Confederate army, especially early in the war, mixed batteries could prove a hindrance, especially with obsolete Model 1841 6lb guns often compromising half of the battery. During a pursuit in the Valley Campaign, Jackson had to order individual rifle pieces up from batteries so he could mass fire on retreating Union soldiers in the distance who were out of smoothbore range. This was a rather helter-skelter method of attempting fire control. The Confederates could and would adapt, like at Perryville where Confederate proved tactically superior in one of the few occasions of the war (even with mixed batteries and six pounders) but there was also occasions like the artillery hell at Antietam, where Confederate smoothbores didn't have the range to effectively respond to Union rifle cannon fire.
The Army of Northern Virginia, benefiting from Tregedar manufactoring, blockade imports, and the fruits of Lee's victories, was able to phase out almost all of the six pounders by the middle of 1863 and replace them with rifled cannon or Napoleons. The Army of Tennessee was able to phase out its six pounders under Johnston and Pendleton in the spring of 1864 and by Atlanta most of the Army of Tennessee's field pieces were Napoleons. The Trans-Mississippi rebels continued to use six pounders during the last major field operations of 1864 (and even a few Federal batteries used them west of the Mississippi). Despite these transitions, the Confederates were unable to avoid mixed batteries in most circumstances.