For both it was a refuge from LA's limitless bounty of drugs (Bowie cocaine, Iggy heroin). Bowie also said it was one of the few cities where he could go unrecognised. The musical consequences seem to have been a side-effect of the substance & fame de-tox, reflecting the austere local surroundings rather than Germany's own 1970s experimentation.
There was actually a recent issue of TapeOp that had a few interviews that went into this in depth, but one big draw was Hansa Tonstudio.
It was a gorgeous-sounding room, built in 1913 as a performance space, used by the Nazis for propaganda concerts, but due to the vagaries of post-war politics, became sort of isolated in what had become a quiet, out-of-the-way neighborhood - you could see the Wall from the windows.
Add that to some of the great German gear the place was stocked with, and you had a winning combination for a creative artist looking to do quality work - enough distractions to have fun (Berlin was still a world-class city) but enough quiet to not be distracted, and all the sonic ingredients to make a legendary album.
The roster of artists who recorded there go from Bowie and Iggy to Depeche Mode, REM, U2, Nick Cave, Pixies, Supergrass, Siouxsie and the Banshees, Nina Simone, and on and on.
(I think Bowie and Iggy recorded in one of Hansa's other buildings first, but the point still stands: great spaces for recording in just the right kind of metropolis.)
There was also this.
Although not specifically from Berlin, Kraftwerk brought "krautrock" into global consciousness in 1974 with the success of "Autobahn." They've been called one of the most influential pop groups of all time, bringing electronic music (prior to the 70s, mostly in the realm of experimental conceptual art or else novelty records) to a pop-song audience.
I don't know if Kraftwerk ever recorded at Hansa, but another krautrock band, Tangerine Dream, did - they were based in Berlin.
The idea of Germany as a place where new and different music would be made was kind of in the air at the time.
EDIT TO ADD: Here's a video of Iggy Pop enthusing about Hansa Tonstudio - it's a commercial thing for a contest, but has some nice footage of the rooms and kinda shows his affection for the space.