In Ulduar, hard modes were triggered by an in-game mechanism that was unique to each fight. For example, Yogg had the Keepers, Thorim had the race in the tunnel, and Mimiron had his Big Red Button.
With Trial of the Crusader and ICC, the hard mode trigger was changed to a switch on the interface. This was done to make creating fights easier on the developers, but it has resulted in qualitatively worse raid fights and hard modes. Hard Modes in ICC are uninteresting compared to those in Ulduar, and mainly consist of the boss hitting much harder, having more health, and maybe one new mechanic.
Ulduar hard modes were better because they told a different story than the normal mode fight. This is because the in-game trigger causes the fight to have a determinant phase. And how the determinant phase unfolds changes the story, and seems to have encouraged the developers to make a more interesting hard mode. For example, reaching Thorim before Sif leaves, causes Sif to jump down and join the fight. It makes sense story-wise, and adds a new element to the fight that is not simply more health,damage, or a new debuff.
The determinant phase is not always part of the fight. For example, on Flame Leviathan, the determinant phase is the towers before the fight. But again, the determinant phase causes the hard mode to change in storyline, which results in a better fight.
It's interesting to note that the one Ulduar hard-mode that is generally regarded as worse than the others is Hodir, and Hodir's hard mode does not have a determinant phase. It's a straight timer, and thus is much less interesting than the other fights.
The determinant phase also had the advantage of tying the boss fight to the rest of the instance. As good as the Lich King fight is, for all intents and purposes the rest of ICC may as well not exist when it comes to the storyline of that fight. In contrast, Yogg's hard mode involves the Keepers that you rescued, strongly tying Yogg to the rest of the instance. In Ulduar, the boss fights feel more a part of the instance, and I think that is in large part because of the way the hard modes were designed.
The in-game hard mode triggers are a much better mechanism than the interface trigger. It may have been harder for the developers to make fights, but they rose to the challenge in Ulduar, and it resulted in much better fights and a more engaging raid instance as a whole.