We've been running Against the Giants and we're most of the way through G1, expecting to wrap it up next session. Conversion of G1, from 1e to 5e, took me less than an hour right before the first session. If anything, my conversion made it a bit too easy combat-wise (the characters started at 8th level) but I'm not sure if that's because of the conversion or because the group has been playing it pretty safe, avoiding direct confrontation as much as possible. There's been a lot subterfuge (unusually much for this group).
While I'm running the original 1e version, I used the 4e version for comparison while converting, but the only thing I remember using was the change from Orc to Dwarf slaves (hillbilly/barbarian Dwarves), as I had just introduced D&D Orcs to my players in my previous campaign as absolute monsters and savages and I didn't want to contradict that image of Orcs I had just established right away.
Well, soon as my players discovered the Dwarven slaves, they immediately starting seeding a rebellion, which I'm not sure they'd have done if it was the Orcs.