Well Hood shouldn't have hared off to Tennessee if he was so keen on fighting Sherman. Based on his pointless assaults against Thomas, Hood did a lot more damage to southerners than Sherman ever did.
Agreeable, however, that is primarily on hindsight. Based on the below correspondence between Grant and Sherman Nov 1-2, 1864, Hood attempted a cat and mouse game, that initially drew concern from Grant.
Sherman initially discussed the difficulty in pursuing Hood. I tend to believe Sherman apparently over dramatized the situation with Hood in order to sell his plan to march to the sea with Grant. Regardless, the planned destruction of Hood's army initially rested on the shoulders of Thomas, via Sherman, rather than Hood himself.
From Sherman's memoirs:
CITY POINT, November 1, 1864—6 P.M.
Major-General SHERMAN:
Do you not think it advisable, now that Hood has gone so far north, to entirely ruin him before starting on your proposed campaign? With Hood's army destroyed, you can go where you please with impunity. I believed and still believe, if you had started south while Hood was in the neighborhood of you, he would have been forced to go after you. Now that he is far away he might look upon the chase as useless, and he will go in one direction while you are pushing in the other. If you can see a chance of destroying Hood's army, attend to that first, and make your other move secondary.
U. S. GRANT, Lieutenant-General.
My answer is dated:
ROME, GEORGIA, November 2, 1864.
Lieutenant-General U. S. GRANT, City Point, Virginia:
Your dispatch is received. If I could hope to overhaul Hood, I would turn against him with my whole force; then he would retreat to the south west, drawing me as a decoy away from Georgia, which is his chief object. If he ventures north of the Tennessee River, I may turn in that direction, and endeavor to get below him on his line of retreat; but thus far he has not gone above the Tennessee River. General Thomas will have a force strong enough to prevent his reaching any country in which we have an interest; and he has orders, if Hood turns to follow me, to push for Selma, Alabama.
No single army can catch Hood, and I am convinced the best results will follow from our defeating Jeff. Davis's cherished plea of making me leave Georgia by manoeuvring. Thus far I have confined my efforts to thwart this plan, and have reduced baggage so that I can pick up and start in any direction; but
I regard the pursuit of Hood as useless. Still, if he attempts to invade Middle Tennessee, I will hold Decatur, and be prepared to move in that direction; but, unless I let go of Atlanta, my force will not be equal to his.
W. T. SHERMAN, Major-General.