It’s always been a nice question as to who won (and lost) the battle of the Wilderness. Much depends on how you define the problem as well as how you define winning and losing. For those who think that Robert E. Lee won, they point to Lee fighting Grant to a standstill while inflicting heavy losses, just like he had at Chancellorsville the previous May.
However, it’s fairer to say that on the battlefield proper, Lee and Grant fought each other to a standstill. Had Hooker not withdrawn in May 1863, Lee would have attacked the Union position once more (and, given that the position was protected by earthworks, perhaps the outcome would not have been what some call Lee’s greatest victory). Thus, it may be fairer to say that the Wilderness was a tactical draw, as neither side held the advantage. Then again, if that’s true, many Civil War battles were tactical draws, with the winner and loser determined by what happened next. For example, this would be true of Antietam and Chancellorsville (as fought): it’s what happened next that leads us to pick winners and losers. One might advance the same argument for Gettysburg, although I think that it would be somewhat harder to make.
What is different about the Wilderness is that from the beginning Grant envisioned it as the first in a series of battles that together formed a campaign. Grant’s strategic objective would not be achieved in a single battle; moreover, at the time the Wilderness was fought, opportunity beckoned for Union success elsewhere (ten days later people would understand things differently). In truth, Grant had achieved what he had set out to do: he had taken the initiative, crossed the Rapidan, engaged Lee in battle, avoided defeat, and retained the initiative to fight again. Indeed, one might say that his initial instructions to Meade–that where Lee went Meade would go also–got things backwards. Where Grant went, Lee had to go, or he’d risk a major defeat.
In June 1863 Robert E. Lee launched a campaign to seek decisive battle through a series of engagements against portions of a strung-out and poorly-led foe. As we know, that did not quite turn out the way Lee had hoped it would. In Lee’s eyes, however, the campaign was the means, the battle the ultimate end. Grant reversed this in 1864: engaging in battles was a means (so was maneuver) to achieving the goal of the campaign. People might still expect a Waterloo, but Grant expected something different. Much like the Vicksburg campaign, where a series of battles served the larger ends of a campaign (and a campaign that looked far more like how Lee wanted the Pennsylvania campaign to turn out than the actual Gettysburg campaign), Grant sought to achieve certain goals in the Wilderness, and did so. When he broke off fighting, it was not because he was defeated, but because continued fighting did not serve his ends.
Lee may have fought Grant to a standstill, but that was all. The rate of attrition at the Wilderness over the long run actually favored Grant; Lee had failed to capture the initiative; and Grant advanced rather than retreated. What made Chancellorsville a Confederate victory was Hooker’s decision to retreat and regroup; what made the Wilderness a Union victory, in the end, was that Grant achieved his aims and continued to advance. The Wilderness served Grant’s ends: it did not serve Lee’s.