I can only speak for Hannibal, as I never really studied the others.

Hannibal would fit in your latter profile. His personal trait was that he was incredibly skilled in reading both, the terrain and the enemy. He knew that Rome focused on deploying as much infantry as possible overrun the enemy and then rout them with cavalry.

Hannibal on the other side was fielding one of the best fighting forces in the world, with less numbers (~45.000) but far more expierienced veterans of hannibals campaign in italy and a good number of wild tribesman from italys north (which werent trained as good but carried a deep feeling of hate towards the romans). Especially his Numidian Cavalry was feared among the romans as they brought some of the most horrible defeats Rome ever took with them.

As one example during the battle of Cannae Hannibal was facing one of the greatest army Rome ever assembled (~85.000, thats 16 legions). The battle was fought on a large plain with enough ground to deploy the massive armys both Rome (more exactly Gaius Terentinus Varro and Lucius Aemilius Paullus) and Hannibal were fielding that day.

Hannibal knew that the Roman Army was counting on their numbers and wanted to simply overrun Hannibal and make up for the losses the Romans took in the past.

Hannibal made use of his numerial disadvantage and deployed his army in a way in which the bigger army of the romans would get into a struggle because of their lack of mobility. He deployed his Infantry in a straight line and made the Roman army crash into his lines. Hannibal ordered his men to not give ground under all cost. His veterans made up his flanks while Hannibal himself was holding the center with the tribesman as a sign that if they were to be overrun Hannibal himself would die with them.

The Romans came crashing into Hannibals alliance. And as Hannibal planned his Veterans didnt give up any ground while the less trained wildlings were pushed back a little causing the Roman Army to start a push to break through his lines. And here is where Hannibals understanding of battle came into play. Due to the ground Hannibals center gave up the straight line shaped into a crescent with the romans in the center.

Meanwhile Hannibals cavalry drove the Roman cavalry off the battlefield and moved up into the back of the Roman army pushing into Hannibals Forces. The Cavalry charged into the back of the Roman army and with Hannibals Veterans still in place the Roman army was in Hannibals Trap.

Hannibal pulled of something that is to this day one of the biggest achievements in warfare, the encriclement of a larger army by a smaller one.

Hannibal slaughtered the Roman forces by squeezing the enemy so tight that it is told many couldnt even raise their sword to fight back their murderers. It is reported that many Romans begged for their allies and friend to kill them instead of having to go through what would have been to them hell on earth. Of the 85.000 men rome deployed that day only 5.000 escaped the battle alive, with 10.000 more being captured.

If you want to check out more about Hannibal this playlist is absolutely brilliant.

Edit1: Completed the text

Edit2: Why am I being downvoted....

Edit3: Changed out some mess ups

Edit4: People seem to want sources so here I go. They are in german however (as its my main language).

First one is Zeitreise 1. This book was my very first history schoolbook. Its for kids but it sparked my interest in Hannibal, doesnt have a lot of facts however, just one of those deployment-graphics you see pop up on Wikipedia aswell. ISBN 3-12-411020-X

Second and last one is the book I bought to do my homework on the topic in 11th grade. Its called Hannibal: Das gescheiterte Genie (which translates ~ Hannibal: The failed mastermind). Its a good read, offers some insights into what we now about Hannibal and argues about what we dont know about him. ISBN 3805345402

Edit5: Im currently looking up some english sources on the matter so you can check them out :)

Edit6: Some links that might be interesting for the english reader: 1,2,3

It's a little of both, actually. Here's some examples:

Napoleon could adapt to many changing situations, and did, but one of his favorite and most revolutionary tactics that was a total game changer was called the Grand Battery. He would concentrate all of his artillery together, and focus them all on one target, overwhelming said target with a massive barrage of artillery fire, and if it was a regiment they'd almost always retreat or die. He had several other really, really, innovative tactics, but that's just one example.

Another good one is Alexander. His strategy was constantly changing as he was forced to fight different enemies in different regions, yet he had two very innovative tactics he relied upon to win battles because they were such a game-changer. First: The Companion cavalry, which were the world's first shock cavalry, many of whom were Alexander's closest friends, and Alexander himself frequently led their charge. Second, his pikemen, whose greater reach due to longer weapons and good training made them the bane of spearmen, especially hoplites, whose reach couldn't beat the larissa spear. (Which is why he and his father managed to conquer Greece in the first place) He used them together, and the pikemen would pin down the enemy while his fast yet dangerous cavalry swung around and hit the enemy from the side or from behind, almost inevitably forcing a rout or complete annihilation.

Can't personally speak much for Hannibal or Caesar. I'm definitely familiar with them, but not enough so to give a good assessment of it. But I'd say, in general, that they fall into the same category as Napoleon and Alexander here.

And, like you said, Nazi Germany is an excellent example of this.

One reason why the Nazis were so successful was not only because of their revolutionary and devastating tactics, but also because of their ability to adapt to a new situation and fight effectively, thanks to their mobility and exceptional skill. Rommel is a very good example of a German general who fought like so.

So, in general, I'd say that the key to becoming a great general is to have both revolutionary tactics to shake the enemy up and devastate them, but also to adapt to changing environments, because what good is your tactic if it can't work for you?

Hope this helped.

Another question, and more specifically in regards to Napoleon, i've heard people say and briefly read that he was so successful largely due to his 'infantry column' attacks wherein he would simply march his infantry, formed in columns and heedless of causalities, straight at and on through the opposing armies troops, who where generally formed in lines. The French columns would break through the opposing lines and cause a route, chaos, and ultimately victory.

Is this an accurate assessment? And if so, how large of a factor was this 'column formation' tactic to Napoleon's military success compared to, as Schrodingersdawg puts it, quick, intelligent reactions, and things of that nature?

Well, here are a few generalizations:

Alexander and Frederick (both called the Great) were prone to using the Oblique order. They concentrated their forces on one flank, or one point, and refused the other parts of the army (if the enemies wheeled their army around to attack the reinforced flank, they would be exposing their own flank and rear to the Macedonian and Prussian armies). They could thereby get local superiority against a numerically superior army and then proceed to roll up the flank.

Napoléon believed in concentrating his fire "on a single point" and then breaking the equilibrium (so, upset the enemy's balance, thereby demoralizing and breaking their will to resist). In addition to that, the French army was simply faster than their opponents when it came to maneuvering as they avoided using baggage trains (which wasn't a Napoléonic invention, however). Napoléon also tried to leave as little to chance as possible - he tried to calculate for all possible situations, although sometimes things happened that were beyond what he had calculated for.

I can speak a bit for caesar. There were two wars that really set him apart. One was the gallic wars, the other was the civil wars. In the gallic wars, the common tactical thread was how the Romans fought battles compared to barbarians. The Romans were opportunistic killers, and fought as a single unit, while the gauls and Germans were much more in favor of man on man combat, fighting individually. This would be exploited throughout the gallic campaign. But this trait was not Caesar's specifically, all roman commanders fought like this. The thing that set Caesar apart was his ability to adapt to various circumstances. During the battle of bibracte against the helvetii, he placed the native auxiliary forces not at the front, but at the rear of his forces, as their loyalty could never be counted on. During the battle against the nervii, in which the Romans were ambushed while setting up their camp, soldiers would rally not to their own standard but to the first one they found, and Caesar had his hands full trying to organize an army not ready for battle. At Alesia, he simply held the line, encouraging his troops, until his lines were ready to break, at which point he attacked the averni relief force of 60k with 6000 cavalry in the rear, completely routing them. He had to fight against the Germans, who would jump off their horses in the middle of battle instead of fighting mounted, and he fought the Britons, who used war chariots in a similar fashion. No single tactic could have effectively dealt with all of Gaul.

During the civil wars, Caesar's great generalship is truly known, as he was fighting other Romans who fought just like him. Not only that, he was fighting Pompey, who himself had conquered from Asia to Armenia and Judea. Pompey who had been given a three year mission to defeat the Mediterranean pirates and finished it in three months. Caesar proved himself at the battle of pharsalus. Pompey had more men, more cavalry, more supplies, and more food, yet still lost. This is mainly attributed to a tactic Caesar used in this battle in which he mixed spearmen in with his cavalry. When Pompey's superior cavalry attacked Caesar's, Sparta got shoved in their faces and they were routed.

Caesar was a military genius, through and through. His victory over the gauls might be attributed to general roman superiority, but that cannot be said for the civil wars. He snapped victory from the jaws of defeat so many times I could see why many believed Fortuna favored him.

Removed because of the breadth of scope which violates rules on trivia seeking and throughout history. If you resubmit this question and limit it to one specific general, this would be more allowable. Right now you're asking us to compare a vague "broad" similarity between military leaders of immense diversity in style, composition, timeframe, and environment.