This list takes a Moneyball approach to rating generals. Wins above replacement (WAR!!). It is a pretty good list imo.
https://www.wearethemighty.com/history/best-generals-ranked-by-statistics?rebelltitem=3#rebelltitem3
Lee has a negative career WAR number. Sowwy.
Grant is the only American to crack the Top 10. I think that's about right too. His is by far the best general we've produced. I'd put Sherman second after him among American generals. Longstreet was easily the best of the Confederate generals.
Well we are definitely gonna disagree on this I can tell. WAR really has no place in a comparison like this, since WAR is a much less dynamic setup. Put Grant in there in 1861 and see how things turn out. By the time Grant took over Lee's forces were permanently crippled after Gettysburg. It would be like saying Snit is the greatest ever after this season (if there is one) when he goes .500 through about the 1/2 way point and then there's a COVID outbreak and every team the Braves play during the second 1/2 of the season is decimated by COVID based DL stints. I'm not a Lee is God kind of guy believe me. I see his positives and his limitations. Lee was great because he was the "aloof general" who had respect but didn't mingle all that much. It gave him more of an aura.
Nathan Bedford Forest was a piss-poor human being but a great tactician though he was practically illiterate, tactics he invented during the Civil War were used during every war since then. Stonewall Jackson was a genius at offensive warfare but a lot of his success was based on his own personal charisma. He was as great at being a general as he sucked at being a teacher at VMI before the war. If Jackson were to be put in Lee's place he would probably have sucked at that too. Too much stuff to think about and manage and he couldn't just go "git-r-done" like he did while commanding the Stonewall brigade. Sherman was really good if you like the old Russian scorched Earth in reverse policy. McClellan was one of the best ever at building and preparing an army for success, he was just absolutely clueless as far as using them in battle. I think he had too much of a conscience.
If you want to go with a Union general who was underrated I'd say Meade. He wasn't flashy or spectacular, he was just solid and fundamentally sound.
If you want to go with a US general from the 20th century I'd have to go with Patton. He was a crazy SOB but he was a "fun kind of crazy" and a genius at offensive tank warfare. I guess you could argue that he was a genius at lots of things if offensive were in the description, at least my uncle would have said so. He was in Patton's 3rd army and hated his guts with a passion.
Wellington's 2 greatest assets were his absolute obsession with Napoleon in every facet of life (he even insisted on sleeping with Nappy's mistresses to prove he was better) and the fact that Napoleon never put his whole strength into the fight against Wellington's "squares" at Waterloo because he feared the Prussians would return and attack the rear of his army. Around 4:00PM that day Napoleon had Wellington on the ropes, but hesitated for almost an hour before he sent in his own personal guard as reinforcements (after Wellington had almost an hour to rebuild his defensive position). Napoleon never sent his whole army into the fray because he feared the Prussians would show back up and hit his army in the backside. It was his ultimate undoing. I've always found that it's good to look at something besides just numbers when evaluating military stuff. Numbers can be misleading or at least that's the argument I used to try and use with my HS math teacher. lol
I'd be interested in knowing who else was on your genius boy's list of greatest generals, just for debating purposes.
EDIT: I looked at your list. Frederick the Great's accomplishments cannot be over-rated but IMO he was. He only won his greatest accomplishments because Russia was ruled by Peter III, or Peter the nimrod might be a better term, just ask Catherine. I'm not that up on the Islamic general or the Japanese general. Absolutely no argument with Julius Caesar or Hannibal. If Hannibal had one single ounce of diplomacy he could have beaten Rome once and for all. Caesar, in battle, was as good as any who ever lived.