Well OP it depends on what you want from each DLC.
Dead Money has a decent amount of new items but by far not as much as the other two.
It on the other hand focuses on giving you a challenge and to give you new gameplay mechanics that you have to figure out (The bomb collar and speakers along with the deadly poison gas).
It has great exploration aspect as you are truly rewarded for exploring in it.
Why?
Cause in this DLC your equipment is removed (but not in the other DLC's) so with the deadly enemies and poison gas you're going to have to scavenge for supplies to survive which makes exploration all the more viable.
And finally it's story, characters, choices, endings sliders, writing, atmosphere and quest design is all top class.
I don't like the other two DLC's so much so this might be a bit bias but I'm gonna try to keep it neutral:
Honest Hearts doesn't exactly do much in the quest design department.
It's very short (storywise), doesn't have a lot of choices until the end and it's mostly built up of fetch quests.
It on the other hand has a new area you can go back to any time you want to, a looot of new gear and a ton of new Survival recipes.
It's writing is good enough, Randall's story is amazing, but it has no pacing and everything happens far too fast, can be over before it even starts.
If you're aiming for a DLC with a unique new area, lots of exploration and lots of new enemies to shoot at then this one is for you.
If you are out for a DLC with a long meaningful story with lots of choices and interesting quest design then this one is not for you.
Old World Blues follows HH's design.
It's story seems absent most of the time and it's choices are very linear (I thought so).
It has a greater emphasis on combat and exploration, and while it rewards you for that exploration the combat can get tedious.
See, the enemies scale to your level so you'll fight bullet sponges if at lvl 40 when you enter it. (I did, had to turn the difficulty down to Normal, not cause it was hard, but because it was tedious and my ammo wasn't gonna last through the entire DLC.)
Has lots of new items though I didn't find any to be spectacular enough to be useful.
Oh and it has a completely overpowered new house for you to use with a vendor, bed, book/pen/clipboard/toaster/mug recycling machines, repair NPC, workbench, reloading bench, jukebox, autodoc and a little garden for you to use as well.
If you want a DLC that has a great story then go with Dead Money, if you just want to shoot a bunch of tribals or robot scorpions and explore then go with Old World Blues and Honest Hearts.
/opinion.
Not really sure why they weren't released in that order tbh..
Nah Dead Money came out before Honest Hearts.