Chickamauga OTL was one of those battles only saved by being the winner. Even OTL, the Union suffered less casualties (slightly over 11k dead+wounded versus 17k, but 3k more missing/captured), despite being pretty roughly handled at the end. If the Union manages to stall Longstreet's attack, maybe by not messing up their line filling a non-existant hole, could be pretty bad. Plausible near 2-1 casualty ratio in a scenario where the Union wins, which would be the worst Confederate field defeat of the war. This moves things up several months, but it may be getting a bit late in the year to start a campaign for Atlanta. Rosecrans obviously will have a great reputation ATL, this is right after his Tullahoma campaign after all. I could see him doing quite well in the maneuver+feint style of working toward Atlanta. What happens with Grant? Vicksburg is wrapped up. Maybe he comes east early, though he was reluctant? Or maybe without reinforcements being needed for Chickamauga there is a campaign in Mississippi/Alabama or something? I assume Bragg is out, given his crushing defeat even given Davis. But who steps in? Johnston just messed up Vicksburg campaign, Longstreet is tainted by defeat as are Bragg's subordinates.
I could see the end of the war being meaningfully accelerated if Rosecrans manages to get in another campaign before winter and take or get close to Atlanta. I think Grant gets too much credit for defeating Lee versus Sherman being in North Carolina and associated problems flowing from that. But fundamentally Confederates are in for a bad time once Union gets through the mountains there, though less bad if they don’t throw away their army for the fun of it (Hood!). Though Rosecrans seems to have been a bit reluctant to advance. But in a Union victory situation the Confederates will be pretty mauled and that should be pretty clear.
I could see the end of the war being meaningfully accelerated if Rosecrans manages to get in another campaign before winter and take or get close to Atlanta. I think Grant gets too much credit for defeating Lee versus Sherman being in North Carolina and associated problems flowing from that. But fundamentally Confederates are in for a bad time once Union gets through the mountains there, though less bad if they don’t throw away their army for the fun of it (Hood!). Though Rosecrans seems to have been a bit reluctant to advance. But in a Union victory situation the Confederates will be pretty mauled and that should be pretty clear.