I'll assume that Beauregard is removed by Davis later on in a similar manner to what happened IOTL and that Hardee takes command at the same time Bragg did historically.
In the short term, it's hard to know what Hardee would have remained in Mississsippi to contest Grant or shift the Army of Tennessee to Chattanooga to block the Union advance there. He wasn't a bold general like Robert E. Lee; they didn't call him Old Reliable for nothing.
Generally, though, this would be good for the Army of Tennessee. One can imagine Hardee in command with Cheatham and perhaps Breckinridge in command of the two corps.