I think for me the biggest difference is not trying to keep track of mechanics and story at the same time. In HQ you can focus on what makes the story interesting, and the numbers are dead easy (HQ2 even has a system for figuring out appropriate target numbers for you, should you choose to use it). So if you expect the characters to investigate who in the clan could be using chaos magic, but really all they seem to be in the mood for tonight is to go hunt down the raiding scorpion men--no problem! You don't need to desperately generate stats for a squad of scorpion men, just adjust the story to the appropriate challenge level for how things have been going (if the blow their scouting and end up getting captured, give them an easy way to escape, while if everything has been going easily add in a scorpion man champion to make the final fight more impressive, etc).
Really gifted narrators that I've played with seem to be able to handle this in any system. For me, however, I find it far easier in HQ.
Having said all of that, if your players mostly just want to know when to roll the dice and how much loot they get off the corpses, HQ is probably not the right system.
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