Beyond the idea of the battle being fought in a wilderness, there is only the slightest of comparison's between the two.
Let's do some comparisons:
In the Teutoburg Wauld, Arminius had between 15-20,000 Germanic warriors, with Varus having between 14-22,000 Roman legionaries and auxilia. At the most generous, Varus only had a 31.82% superiority over his foes, at worst, he was outnumbered by 30%. At the most equalized amount with both sides at their peak estimated strength, the Romans only had a 9.91% superiority over their foes. In other words, the Massacre of the Iron Legions was a much more evenly matched affair than what was in the Civil War.
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The plan: Grant never intended to battle in the Wilderness, he was just using the Wilderness as a quick shortcut. It was only the slow movements of the AOTP that meant he didn't break out. This was also Varus' intention as he marched to put down the rebellion rebellion of a local tribe.
That's where the similarity ends.
Varus was unfamiliar with the land, so he relied upon his native scouts, especially the advanced auxilia under Arminius' command, where as the idea of local guides seemed not to be used by the AOTP, possibly because of familiarity with the area due to the Battle of Chancellorsville. Arminius always planned to trap the Legions within the Wauld, and as such had already set up his coalition within the forest to spring the ambush. Lee's intention was also to trap the AOTP in the Wilderness, but that was
only if that was Grant's direction of march and only moved towards the Wilderness when he was assured of the movement. As such, the battle that was fought had more in common with Washington's movements during the Philadelphia Campaign of 1777 then with the Germanic Revolt.
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The commanders involved: Publius Quinctilius Varus was both a general and a politician. His reason for being in Germania was because he had already upset the people of the province of Judea by conducting mass executions of rebels, and had been lounging in Antioch before being sent to the "pacified" Germania by Augustus as the Roman Legate for that province. Arminius had spent years in the Roman military and had long since been planning to lead a revolt against Rome.
Ulysses S. Grant was a soldier, plain and simple. However, unlike Varus, he was the overall commander of the Union forces. Whereas Varus only had direct control over those legions within his own province, Grant was the grand poohbah and everything was his to do with as he pleased (within the bounds set by the Government). Lee had also served in the Union military, yet he never plotted to lead a revolt against the US until Virginia seceded and even when he became the leader of the ANV, he only had command over that army until the very short period where he was the supreme commander of the Southern military. Arminius on the other hand basically had free reign over the Germanic coalition, as long as they would follow him (which was for several more years).
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That's not even comparing the geopolitical realities of the situation. That's not even taking into account the final result.
So while the very basic premise of a comparison between Teutoburg and the Wilderness is interesting, it unfortunately is only drunken-goggled deep.