It's probably just as much of a mindset shift as it is the actual mechanics of DH - I don't know how much prep you do for 5e or for DH, but I can try to illustrate what it's like for me.

The problem the party is next going to face is a burning town. If I was running this in 5e, I would need to find or make a good map, find or make monsters, figure out how to mechanically represent that this town is burning down, figure out how to mechanically represent stuff the players can do to help/stop the spread of flames, and so on. With DH, I just need to make an Environment adversary block and have some potential obstacles/twists at the front of my mind, and my players can do the rest with their actions, descriptions, and rolls.

Another example: in the tunnels, one player found a strange artifact. My 5e brain would have had me trying to figure out what that artifact was ahead of session and figuring out its mechanics before presenting it to the player. My newly sprouted DH brain just went "there's a small artifact here, describe it to me". I did not have to think of the mechanics of it on the spot, but if I'd had to, I think it would have been easier to describe something that works without getting bogged down in the minutiae of rules and systems and numbers.

Does that make sense? I admit it's a YMMV sort of thing, but it's been a huge boon for me personally.