Forrest was the devil in a saddle. He certainly was a cavalryman. I forget what battle is was in Mississippi when Stephen Lee was in charge and attacked 11,000 well entrenched Yankees with his 8,000 man force, against Forrest's advice. After the battle Forrest said to Lee "Don't feel bad general, if I had me a West Point education the Yankees would be whipping me too." Maybe it because Forrest had no military training that some folks say he was not a cavalry officer. He certainly rewrote the book. Erwin Rommel studied Forrest, so did George Patton.
That was Tupelo - Forrest was plenty mad at S D Lee as he was against the battle. Got to say, though, Forrest made a serious error that probably finished the battle for a loss. He also noted West Point again when talking to a couple of Wilson's aides before the battle of Selma - Col Parkhurst and Capt Hosea. Forrest offered a 'nice little place' for a fight between him and Wilson, any time Wilson thought he was ready, and remarked he carried 'nary a saber' in his command. Hosea pointed out that as a graduate of West Point he believed in using them. Forrest replied, "I ain't no graduate of West point, and never rubbed my back up against no college, but Wilson may take his sabers and I'll take my six shooters, and agree to whip the fight with any cavalry he can bring."
Methinks he doth protest too much! The old 'sour grapes' harumph. I think if Forrest had been able, he would have gone to West Point and happily learned how to soldier. Every time he got the chance, from teen years on, he would join a military operation if there was one. Born that way!
Custer on the other hand kept skating as close to the edge of getting kicked out of the place as he could. He'd collect demerits right up to the last one, then straighten up and work them off. That was one of the reasons he ended up in the cavalry...which was right where he wanted to be. There's some speculation he might have been a bad boy deliberately so he wouldn't end up an engineer.
Since the Little Big Horn was mentioned earlier, I'm not sure that proves Custer was a lousy commander. Definitely had a bad day! There seemed to be problems with his command that were similar to some Bragg faced - subordinates who were undermining him or passive-aggressive about obeying. And, Custer didn't know what had happened to Crook just before over there on the Rosebud. A head's up that every Indian on the Northern Plains was sitting down in that gully would have been appreciated! Truth is, Custer didn't exactly lead his men to their deaths from his own vanity but from a fatal underestimation of the enemy he faced. Crazy Horse was one of the best generals of the day but Custer saw him as a nekkid savage with no discipline leading other nekkid savages. Fatal mistake.
The whole situation of the Little Big Horn would not have existed if Forrest had been the commander. He was such a completely different person it's really hard to compare the two commanders. I do believe Forrest had a better understanding of the capabilities of Natives. He had Cherokee relations and had several Indians among his troops. I don't think he would have thought Crazy Horse, Sitting Bull, Gall or the rest of the Plains war chiefs were any sort of a piece of cake.