Alright, so allow me to put in my 3 cents (not 2 cents... you all know me. It's more than 2 cents.)
First of all, I agree with Auto on most of what he said. Took the words out of my mouth. However, in the interest of turning this debate upside-down and creating a little more discussion, I'm going to talk favorably about the DH.
BEFORE I DO, however, I want to say that I do, in fact, use the regular launcher, and I do think the DH is highly situational. I just want to get some devil's advocacy going on here.
The direct hit is ridiculously powerful. If you've spent the time practicing to get your aim up there, and you've spent the time getting used to the increased speed, both in rocket jumps and in combat, you can be a very, very deadly weapon with that thing. Notably, it only does about 112 damage at a mid-range, but it DOES experience damage ramp up; it maxes out at 140 damage at close range. I'm sure you've all experienced it, so I don't really need to say it, but that's plenty to 1-shot a good number of classes.
hook it up with the buff banner and we're talking about 151 damage per shot; that's enough for gunslinger engies as well, and it's certainly enough to make a fully-charged medic rage quit. It's crit of 338 is enough to kill anything that hasn't been overhealed. ANYTHING.
Now, many of you are complaining about the fact that you can't aim into a crowd and kill them all like you could with the regular rocket launcher; that's true. However, assuming there were 2 people standing right next to each other, it would probably take 2 or more rockets with the standard launcher to take them both out, if you were aiming at their feet. It would also take 2 rockets with the DH; the difference is that you don't aim them both in the middle, you aim them at the individuals. And that brings a very important theory up.
Think about all of the RPGs you've ever played. Think about final fantasy, when you're fighting 3 monsters of equal strength, and you don't have anybody in your party who can hit them all at once (someone screwed up on the party creation screen). What do you do? Do you focus your blows, or do you distribute them equally throughout the party? Any experienced player will tell you that you systematically eliminate them one by one, instead of killing them all at the same time.
Why? Simple. Hurting people doesn't reduce their ability to kill you. At all. KILLING people, on the other hand, does. Quite admirably, in fact. When you hit a crowd with a rocket launcher, you're giving them time to react; they're taking damage, they have a little flashy bar on their screen telling them where it's from, and depending on how fast you are, you could potentially be dead without killing ANY of them.
However, if you have a DH, you can 1-shot many lower health classes, and 2 shot basically everyone. Same scenario, with a crowd; instead of tickling everyone, you kill the engineer they were there to protect. Didn't notice you? Then they no longer have a medic. You could do that with the regular launcher, but it wouldn't do much for you, unless you got a lucky crit.
Now, I hear you out there, Auto; you mentioned in your post that you're happy to let your team kill that half-health guy you bruised. Normally, that's fine... if you have team support. However, if you're behind enemy lines and on your own, which soldiers tend to like to do, that half damaged guy is going to go and get health (through a medic or otherwise) and run away from you. More importantly, he'll live to kill you, or your teammates. If you 'snipe' him with the DH, there's no running away; he's gone! No coming back to kill your folks; he's watching a respawn timer.
So, basically, the idea I'm trying to get across here is that damage can easily be fixed, but death can't. When given the choice to partially damage 3 people or kill one, In my head, the choice is fairly obvious. Low health doesn't affect people's damage-inflicting capacity in any way, but death does. They might retreat out of fear for splash damage, but they also might come after you.
The DH, I would say, is the ideal weapon for roaming soldiers with no team support for that reason. If you have medics behind you, and you have a heavy sitting there to help, then yes, the rocket launcher is the best move. After all, it puts out more overall damage than the DH with its blast radius. However, if you DON'T have team support, the DH will ensure more actual kills for your efforts, which will not only benefit you, but also your team.
Oh, and a final thought: everyone's been saying the DH is better for killing sentries; I wholeheartedly disagree. If there's an engie there, the DH can't cut through it any better than the regular rockets can; the engie can still out-heal you. However, the regular rocket launcher can be used to inflict splash damage on the engineer, killing him, and making the sentry basically useless when it comes to rockets of any flavor; the DH can only hope to catch the engie off-guard.
Oh yeah, and this:
I don't know what Auto said but I skimmed a little and I think I agree with him. I make a formal request to Dread and AutoDMC to include tl;dr in every post they make.
I take that as a compliment... and I respectfully decline <3
However, because the point can be ground down so easily on this post, I'll make an exception.
TL;DR: A damaged guy can still kill you. A dead guy can't. DH can 1-shot people, instead of tickling a crowd. 'Nuff said.