If Burnside had listened to Hancock... (I mean as long as we are doing the what-if game) Perhaps, Lee would have listened to Jackson, who wanted the line to be on the North Anna River so he could have room to manuever, which was denied him at Fredericksburg because of the Union guns on Stafford Height.
The point is, the Union was only one error away from annihilating the Rebs at SEVERAL points. And, moreoever, the Confed generals ALWAYS took higher losses percentage wise-—something that simply isn’t supposed to happen to an army “playing defense.” (again, I exclude Vicksburg-—a 100% surrender-—and Fredericksburg as the only exceptions).