As Howard (of whom Wawro is a pale, thesis driven, Prussophilic shadow) points out, the Prussians mounted major frontal assaults in 6 out of the 7 major battles of the Franco-Prussian war and broke through.
In 1870 they were still operating in battalion columns. Breaking down to company columns came in after the initial battles. By the siege of Paris they started using skirmish lines and the like. Most of this was not forgotten but was doctrinally rejected after the Franco-Prussian War. Command and control was all important (rightly so) and so loosening of formations was rejected and the German Army of 1914 made attacks in a looser order battalion column, but still a column.
Rob is correct in pointing out just how pushed down command authority was. A Prussian captain, commanding a body of men that at full strength looks a lot like an ACW regiment has a great deal more latitude to act than a Union colonel. The orders process means that the Captain knows the 2 up (regimental) objectives and schemes of maneuver and so can continue to act in accordance with the main effort even after communication with battalion and regiment are lost.
OTOH a Zug leader is a mere cypher responsible for fire control orders (see Shoulder to Shoulder: Close Control and "Old Prussian Drill" in German Offensive Infantry Tactics, 1871-1914, The Journal of Military History, Vol. 68, No. 1. (Jan., 2004), pp. 73-104 ). Nothing smaller than the company maneuvers on the field.
What Prussia had over France in 1870 was a far superior artillery branch. This comes partially from observations of the ACW (where they concluded the artillery was the decisive arm on the battlefield) and their war against Austria where their artillery got the crap kicked out of it by the Austrian artillery on a regular basis. This, and their superior staff processes, compensated for the general crapness of the Prussian infantry.
In 1861 none of this is really true. The Prussians of 1861 only have 36 infantry regiments (exc/ landwehr) and these are very weak. In a typical battalion of 1,000 about 300 are new recruits, 300 are trained, 300 have been released to civilian life and about 100 have deserted (round figures). Roons reforms vastly increased both the scope of conscription (in 1861, after exemptions, less than 80,000 men were liable for conscription) and the length (in 1861 a typical Prussian soldier served two years with the colours and then went home as a "war reserve", under Roon it became five with the colours).
The Prussia of 1861 is unlikely to want to place itself in a position where it may be fighting France, Britain and many of the German states.