Strange thing, the Prussians, despite their image of "I HAVE ZE VAXED UND POINTY MOUSTACHE UND ZE ZPIKED HELMET! ATTENTION! ACHTUNG, SCHWEINEHUNDE" and Iron Discipline, actually were very flexible in their tactics. They didn't form into long lines and bayonet charge en masse; they attacked in relatively small schwarms (20 man units), using many of those interesting German terms that keep cropping up later: Auftragstaktik, "mission based tactics", for example. Officers were trained to use their own initiative wherever possible (and often did, attacking from several directions at once.) They were issued with maps. And their soldiers were literate, numerate men, who could thus be shown tactical exercises, drawings, models and so on, and they practiced constantly. Hresvelgr, if any army in the world at this time isn't going to blindly goose step in close order towards volleys of bullets and shells, it's the Prussian army. If you want to trust foreign generals about the Prussians, how about trusting French observers at the Austrio-Prussian war, who, although they were impressed by Prussian agility, actually thought that their offensive tactics caused fragmentation as units broke off from line and column on their own initiative. (A foolish misinterpretation.)
The trouble in the Franco Prussian war was the the French usually fought entrenched on the defensive (at least, to begin with- once Paris was besieged, the situation was very different), and the Prussians thus had to attack their positions through a hail of chassepot fire. But here, the Union does not have the same level of French small arms superiority; most of its troops will have muzzle loading rifles (give or take a few repeaters and possibly a handful of maxims), which means the Prussians will be able to use their infantry tactics to a greater effect.
This isn't the army of Frederick the Great, or even of Ligny. This is the army which, using the breech loading rifle and small unit tactics, inflicted 5 to 1 kill ratios on Austrian infantry (with muzzle loaders, advancing in column, but making far better use of their artillery, which was mostly superior to that of the Prussians.) I would also point out that the muzzle loaders didn't to stop the Prussians at Konnigratz, for all their marginal range advantages.
It definitely isn't going to be all for the Prussians, though. At this point (1865?), Prussian cavalry was still "a thoroughly useless ballast on the army" as Moltke put it, which preferred shock charges to proper scouting. (In stark contrast to its superior performance in the Franco Prussian War, where it was actually mostly used for scouting-and did well in that role.) They also lack some of the Union's innovations (such as balloons, maxim guns, and a large navy, if that's going to be worth anything in this campaign-where is it being fought, coincidentally? It it's just "Prussia vs the USA", then neither side is going to be able to actually fight each other.)
I don't know enough about the Union army to be certain, but I'd put the advantage somewhat towards the Prussians, especially if they fight somewhere with railways, and their staff get time to draw up an enormous war plan.