I am not really familiar with the battle but from what I read the Union forces were just as mauled as the Confederates were.
And that early in the war the Confederates were able to replace losses (just like the Union), something they couldn't´t do later in the war
(hence Joe Johnston´s absolutely defensive stance in the East wasn't´t maybe that unreasonable - as the Confederates needed the bigger part of their reinforcements to support Leeds more offensive strategy in the East and just couldn't´t support two offensive armies...)
Because of that I wouldn't detect in that battle a decisive victory of the Union - it just reminds me of a brawl in a pub after the lights went out with everybody punching wildly into the dark, smashing furniture and bleeding noses whose owners were vaguely discerned or just guessed....
Murfreesboro, should you consult a contemporary map, is the center of a Spider’s web of roads that includes the Nashville & Chattanooga RR. Taking that key junction allowed Rosecrans to establish a line 45 miles long from Readyville in the east to Franklin to the west. An all weather “pike” (toll road) ran directly from flank to flank. Enormous earthen fortifications & smaller works secured the southern side of a triangle roughly 45 miles on a side with Nashville at its peak.
By taking Murfreesboro, Rosecrans secured his base at Nashville. Because of the lay of the land, the only approach to Nashville led through Murfreesboro. 20 miles south of there was Bragg’s HQ at Shelbyville. Due to topography, communication from one flank to the other was a disjointed 70 miles. There are only three practical gaps through the face of the Highland Plateau. This forced Bragg to concentrate his forces into three groups that could not support one another.
The Murfreesboro position, due to topography, cut the Army of Tennessee off from its sources of remounts. During the six months from the Battle of Stones River & the Tullahoma Campaign, the quality & number of draft animals & cavalry mounts went into a steep decline. From that point onward, Union cavalry only got better & CSA cavalry got worse.
There were 72,000 slaves in the counties surrounding Nashville. One of the little understood benefits of Stone River was harnessing that labor pool. The Tullahoma Campaign, taking Chattanooga, & the Atlanta Campaign could not have happened without holding Murfreesboro. Topography demanded it.
My point here is that battles are not sporting events where casualty figures are the scores. It is who holds the blood soaked ground & how they exploit it that matters. Sadly, in military logic, lost lives are a means to an end. At Stones River, the loss of life was roughly equal. The strategic impact of the victory was enormous.