It's hard to overstate just how off-base and factually incorrect this analysis is, at least from the Grant side of things. No offense meant to OP, who seems to have been the victim of what was, for a time, a standard Lost Cause interpretation of Lee and Grant, but this view is patently false.

Very quickly on Lee, there's been plenty written on this sub on Lee's abilities as a general and tactician, but to TD;LR things, yes: Lee was a fantastic military commander who demonstrated superb strategic and political acumen. Though far from perfect, and with more than a few tactical mistakes made during the American Civil War (his performance at Gettysburg, his refusal to go west in 1863 to deal with the crisis in that theater, his sometimes vague orders to subordinates), it is hard to imagine anyone doing better with the resources available. So in this regard, OP's history teacher was more or less correct in simplifying Lee as a "well organized masterful technician."

Okay, fair enough on that front - but let's get to Grant. First, the drunkenness. There is no verifiable record of Grant getting reprimanded or otherwise called out on the carpet for being drunk during the Civil War. Despite what Shelby Foote relates in Ken Burns' Civil War doc, there's no actual evidence of Grant going on a bender during the Vicksburg campaign, and while it is POSSIBLE that this happened, let's look at the facts. Rumors of alcoholism dogged Grant throughout much of his Civil War career, stemming from a very real concern about his drinking habits as a young officer in California. Again, no official records attest to this, but it is generally agreed upon by historians that Grant did have a drinking problem, one that became an issue for him when stationed away from his family in the 1850s.

Fast forward to the Civil War. As a West Point graduate and veteran of the army through the Mexican American War and service afterwards, Grant was a known commodity in military circles. He knew other regular army generals, and they knew him. In these circles, promotions and assignments were very competitive, and many of these officers (and their allies/benefactors) actively spread rumors, false or otherwise, to tarnish the reputation of others so as to make themselves look better. What's more, newspapers loved this kind of drama, so a small rumor or some back-stabbing gossip got around fast, and in this way, Grant's drinking became a popular topic when his star was on the rise.

Indeed, think of this like movie awards season: if you run a studio and you have a film in the running for best picture, you might spread rumors about a rival production to make it look bad, thereby increasing your own film's standing. It was no different during the Civil War, and throughout it all, Grant never faltered. Reading correspondence from politicians, fellow soldiers, friends, and family, you're not going to find one instance of a person attesting to having seen Grant drunk during the Civil War. Sure, there was plenty of "I know a guy who knows a guy who said he saw Grant drunk," but that was it.

So yeah, the drunken butcher myth just doesn't hold any water. Was he an alcoholic? Maybe? Grant seemed to purposefully abstain from alcohol in social situations, and there's enough evidence out there to suggest that he was very conscious of the "drunkard" rumors, but for such a famous drunk, there's very little in the way of public, verifiable accounts of him being drunk during the war.

Now, as a commander and tactician, we do have lots of evidence: none of it good for people like OP's Texas history teacher. Bruce Catton wrote extensively on Grant's abilities as an organizer, trainer, and leader during the early days of the war, when he commanded the 21st Illinois Volunteer Regiment (check out Catton's 'Grant Moves South' & 'Grant Takes Command' for more on this). He turned a rag-tag group of civilian recruits into a professional unit, no easy task, and continued to demonstrate his superb leadership abilities in a string of small victories that culminated in his hard-fought victory at Shiloh. I did an in-depth breakdown of his masterful generalship during the Vicksburg campaign here (https://www.reddit.com/r/AskHistorians/comments/9kom99/william_tecumseh_sherman_became_famous_and/), which laid out a blueprint for our modern understanding of "Total War." Lincoln, always known to be unsympathetic and quick to cut bait on generals that didn't grasp the full scope of the political as well as military necessities of winning the war, stood by Grant when the losses of the Wilderness Campaign piled up. I bring this up because it demonstrates that even then, smart minds understood that Grant wasn't just throwing bodies into the meat-grinder, but rather he was executing a series of flanking marches that kept pushing Lee further and further back to a point from which no more offensive campaigns could be launched. Grant's army pool was not bottomless, and those who point to his numerical advantage over Lee at this point disregard the very real public opinion factor that might have just as easily have turned the tide against Grant (in other words, if the Union's losses were as high as they were without quantifiable gains, Grant would have been sacked). Grant knew this, as did Lincoln, and the campaign proved to be a masterful example in generalship that forced Lee into a stalemate from which he never really recovered.

Lastly, Grant knew how to manage an army, and was damn good at promoting subordinates who knew how to get the job done (i.e., Sherman and Sheridan). Sure, Grant had missteps (the last attack at Cold Harbor, the Battle of the Crater), but if you study his campaigns, you'll see a deliberate, thoughtful, calculating commander at work every step of the way.

[Sources: Bruce Catton, 'Grant Moves South' & 'Grant Takes Command'; Jay Winik, 'April, 1865'; James McPherson, 'Battle Cry of Freedom']

I would add to petite-acorn: Grant's administration was one of the most corrupt, but Grant himself was not. Grant made a poor transition from military to the civil service. In the military, he was used to asking his subordinates to be completely loyal- even put their lives at risk in carrying out his orders- and in return he was loyal to them. He thus did not comprehend how much his friends, family, cabinet officials would be tempted to use their connections to him for personal gain. His personal secretary, his brother-in-law, his Secretary of the Interior Columbus Delano, his Secretary of War Belknap all failed him in this way. He did have some lucky choices- Hamilton Fish as Secretary of the Treasury was quite capable, and Grant's second administration was much cleaner than the first. But Grant chose the wrong guys in his first term, and stood by them until the facts of their corruption were unavoidable.

Perhaps a bigger complaint against Grant was that he started with great intentions and good prospects but didn't fulfill them. He began his Presidency as the most popular person in the US, with no Democratic opposition, and stating some truly progressive ambitions: establishing civil rights for freed slaves and creating good and honest relations with the western Indian tribes and with Mexico. After four years of being betrayed by some of his cabinet, and facing opposition from within the Republican party and Southern mobs , he became something of a nondescript bureaucrat, unwilling to get out and campaign for his ideals, instead simply giving up on rights for freed slaves in the face of unified Southern opposition, abandoning honest treatment of the Indian tribes in the face of US citizens' greed for their land... shuffling and stamping papers and making modest speeches. When he came back from his world tour in 1880 and put his hat in for another term as President, he couldn't actually point to anything remarkable that he wanted to do...he just wanted his old job back.

Grant is one of the more fascinating figures in US history. He does not really fit into either category of hero or villain, but biographers have tried to shove him towards one side or the other.. Ron Chernow's biography has recently tried to cast Grant in a more positive light, maximizing his war service and first years as President, minimizing how much power he had over his party and his cabinet. William McFeeley's earlier biography grades him more harshly, as a decent man who was promoted beyond his abilities. I tend to agree with McFeeley: there was no President in a stronger position than Grant was in 1869 for achieving his stated goals, so he should get some blame for not achieving them. And he likely knew this: a telling thing I think is Grant's Memoirs. They pretty much end with his war service, and have only some valedictory remarks on his Presidency, more wishful thinking than policy ( like his notion that it would be better to export the freed slaves to what's now the Dominican Republic than give them rights as full citizens in the US ). It's like he was just tossing around some opinions, knowing they were now irrelevant.

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