Grant at Vicksburg was different. After trying direct assaults his tactics changed to isolation of the roads leading into Vicksburg and then starving it out.
One huge bit of luck for the North was the absence of Gen. Stonewall Jackson. Jackson had died of pneumonia, I believe, while recovering from loss of an arm due to friendly fire at Chancelorsville. On the first day of the battle at Gettysburg, Southern troops under Gen. Euwell — who had replaced Jackson — failed to take Culp’s Hill. Jackson probably would have succeeded.
Lincoln was incensed with Meade when he allowed the tattered forces of Lee to escape rather than cutting them up piecemeal.
Lee should have taken a defensive position like Longstreet wanted.
Luck sure has its place in history, but so does strategy of what is needed to be done in order to carry the day.