Brusilov, hesitantly. Given that Russia was the country closest to the abyss, pulling that kind of thing off that late in the game takes genuine brilliance.
Petain, Ludendorff, Ataturk were all competent but hardly "best"; Haig gets something of a bad rap but certainly wasn't "best"; Lettow-Vorbeck rocks but isn't really directly comparable. Pershing and Hindenburg were nonentities famous because of nationalism, nothing else.
Arthur Currie and John Monash. The two best allied commanders of that war, both leading the two scariest forces in the war, the Canadian Corps and the ANZAC.
I love you.

And Currie and Monash were both
very good - although not really the same kind of front commander as the others, Lettow-Vorbeck excepted.
I know I'm a bit biased being American but Pershing 100%. It was the Argonne Forest that won the war for the allies.
The battle of what now? The one from the massive unified-command campaign where the German army crumbled away like it had been fighting for four years under blockade and the home front was now coming apart at the seams? What did that dude from Mexico have to do with that?
(More seriously: if you want to make the case that America's entry into the war doomed Germany, forcing
Michael as a desperation move and then the collapse of the whole German army afterwards, that's not an untenable position; but in that case you're arguing that America's contribution was "meat! look at the meat! SO MUCH MEAT", and nothing at all to do with Pershing's competence or lack thereof.)