I answered about Wittgenstein and Blücher her: Strange combat results combat result
With Murat and zu Hohenlohe-Ingelfingen, Murat's force is small enough, that they could have broken off before a single shot was fired. But Murat's quality may have allowed him to remain for the start of the battle.
Since both sides are attacking, chance may have given initiative to zu Hohenlohe-Ingelfingen, in which case Murat's artillery may have played a large role in the forest. He has a large cavalry force, and may have had a lot of horse artillery, which will do better in restricted terrain that larger artillery.
So the results my have simply been luck and terrain with regards to losses.
At any rate, Murat's force took a lot of cohesion loss, although no hits, and was either forced into retreat through the cohesion loss, or Murat decided between round that from the cohesion loss, it was time to beat a hasty retreat, and withdrew.