Dead Money on all poll options.
The weapons in Dead Money were actually useful as compared to HH's which didn't fill out an open gap but just stacked more crap upon what we already had.
The quests in Dead Money was actually interesting and I was excited about each one of them while in Honest Hearts the quests were so short and mostly came down to "Go to X and kill/collect a (couple of) Y".
As to the story, I never found there to be a good reason for the Courier to go to this bunker except maybe if she hates radio signals and have an obsessive compulsive disorder to turn them all off. But once inside the story was superb and I really connected with the characters which were all brilliantly written. In HH on the other hand the characters were largely uninteresting apart from Follows-Chalk and Happy Trails and the story felt very halfassed and linear.
And the endings, I liked Dead Money's better, they really had interesting things going on for the characters while HH was very predictable and kinda "meh". I also liked that Dead Money gave me two new final endings, Elijah and Greed.
Now the environment on the other hand they both equalize themselves out. HH was beautiful and DM had a cool as [censored] horror feel to itself.
DM was also more challenging, which is a plus for me.
The exploration in Dead Money is far more rewarding than HH's.
Why? Cause in DM we have to try to survive the death gas and limited supplies and finding more chips is actually useful.
But Honest Hearts feels like it was pointlessly bloated with very few interesting things in it.
I'd rather have a smaller area with more interesting exploration than a larger area with little to nothing of interest.
And apart from the Survivalist and the occasional good loot exploring Zion was not very rewarding.
The companions in Dead Money all felt very fleshed out with lots of interesting things to say about their past and their current situation, but in HH only Follows-Chalk met this standard while Graham won't speak as a companion or do much else and that Sorrows chick was just a boring, tedious, useless pain in the ass.
So Honest Hearts was a fun little timesink while Dead Money was a brilliant masterpiece.
/imo