One of the things that made Herohammer for me was the army composition system. For most armies, you could spend up to 50% of your army points on characters, with at least 25% on regiments. Warmachines, monsters and allies could each have up to 25%, although the Chaos book traded the warmachine slot for daemons, who could go up to 50% of your army points. Yes, you could spend 50% on characters, 25% on regiments and the rest on warmachines (or monsters, for that matter!). In fact, 5th Edition made clear that you could spend the entirety of the 25% allied section on allied characters, which meant that you could feasibly have 75% characters and 25% common troops.
It's important to note, however, that while 3e army composition rules (found in the Armies book) are much more diverse, they are essentially the same as the above. For example, most armies required a minimum of 33% regiments, with at least one character and up to 50% of the points spent on characters. There were some notable exceptions, including High Elves (who allowed 66% characters); Undead, Slann & Dwarfs (minimum 50% regiments and maximum 50% characters; and Orcs, Skaven & Bretonnians (who, surprisingly enough in the case of the Bretonnians, only allowed 33% characters and required at least 50% regiments). The magic items in 3e were also just as powerful as those in 4th/5th, so the possibility to make a powerful army of characters was just as much a part of the earlier editions as it was in the later versions.
Of course, with the possible exception of the dreaded Bloodthirster, huge characters were unlikely to win you a game. Expensive characters could rarely earn their points back unless they battled other expensive characters—something which was just as risky (particularly with dangerous items like the Black Gem of Gnar on the battlefield). Furthermore, risking your army general in combat could have drastic consequences in 5th edition, as the death of the general would cause army wide panic. In this way, 4th/5th was LESS Herohammery than 3rd Edition. While a 3e hero could expect to hit poor, bloody infantry on 2+ (with only a 6+ followed by a 4+ or even worse for retaliatory hits), 4th/5th heroes were limited to 3+ to hit (and 5+ for the lowliest of infantry). The 3e magic item rules were also less restrictive in many ways, as a high level character could wield a fully customized magic sword that cost nearly 300 points!
Heroes in 4th/5th were at some danger when faced by monsters and elite infantry. They almost always had to be safely stowed away in a protective regiment (especially to avoid missiles and warmachines sniping them). Admittedly, however, it was sometimes not clear if the hero was in support of the regiment or if the regiment was in support of the hero, which to me is the essence of Herohammer: you are never quite sure if you are playing a heroic game or a mass battle game. To their credit, 4th and 5th edition blurred the distinction and created a game that was truly "fantasy-battle."
When we played, we normally didn't include big heroes in our armies. When we did, however, we wanted them to do crazy, epic deeds. We did not shy away from the power of Herohammer, but rather enjoyed it quite a bit—it added a fun variant to the usual infantry slogs. From what I heard, however, a lot of players (or perhaps a very vocal minority) eventually got sick of what heroes did to the game. They were incredibly downplayed in 6th edition, but we can already see a corrective to this in 5e, which gave recommendations for restricting army composition (no wizards above a certain level, only one magic item per character and so on). I do not remember playing with these and I wonder if many others ever did (outside of tournaments, where I understand certain restrictions were typical).
