Because they were working from different records. That is the whole answer and everything else is elaboration on it.
The Americans grew up on the New Wave of British Heavy Metal riff, which is melodic, which resolves, and which implies harmonised twin leads. The Germans took their bearings from Venom, Motorhead and one Accept album track, and their model of a good record was something cut in three days by people who could not play.
The reference library

A teenager in the East Bay in 1983 could hear Diamond Head, Iron Maiden and Judas Priest without difficulty, and those bands supplied a specific idea of what a heavy song contains: a riff that goes somewhere, two guitars in harmony, a section that resolves.
A teenager in Essen had Venom, Motorhead and "Fast as a Shark". None of those supply melody, resolution or harmony. They supply speed, filth and the demonstration that competence is optional.
Build a band from each library and you get two entirely different musics from the same instruments, which is exactly what happened.
The production

The second cause, and it is a deliberate choice rather than a limitation of budget.
The American records are dry, close and separated, because a music built from riff sequences has to be legible: you are supposed to be able to take a riff apart while it plays. The German records fuse the guitars into a single mass, let the drums bleed into everything and put the vocal inside the mix rather than on top.
The result is a record that cannot be analysed while it is running, which was the intention. You are not meant to admire the construction. You are meant to be underneath it.
The vocal
American thrash singers shout in pitch: Araya, Baloff, Ellsworth are all producing notes, however aggressively. Petrozza, Angelripper and Schmier rasp, low and forward, with no attempt at a note at all.
That single difference is the most audible thing separating the two traditions, and it is a straight line from there to the vocal of every death metal band that formed in the following five years.
| Bay Area | The Ruhr | |
|---|---|---|
| Built from | NWOBHM riffs | Venom and Motorhead |
| Riffs | Melodic, resolving | Chromatic, unresolved |
| Leads | Harmonised, twin | Functional, or absent |
| Production | Dry, close, separated | Fused into a mass |
| Vocal | Shouted in pitch | Rasped, no pitch |
| Effect | Legibility | Weight |
The conditions
The third cause and the least romantic. The Ruhr in the early 1980s was watching its pits close and its steelworks shed shifts, and the bands were formed by people with a realistic view of what was likely to happen to them.
Tom Angelripper of Sodom worked underground while the band existed. Nobody had a rehearsal room worth the name or money for equipment. These were not teenagers with a plan; they were teenagers with nothing to protect, and the records sound like it.
It would be dishonest to claim the music is about coal. It is entirely honest to say that a scene with no expectation of a career makes different choices from one that can see a record deal from where it is standing.
Which is better
Neither, and the question is less interesting than the pair. Reign in Blood and Pleasure to Kill came out six weeks apart and represent opposite solutions to the same problem: Rubin took everything away so that each blow lands, Johns left everything in so that it piles up.
One is a scalpel and the other is a landslide. Any listener who has heard both and prefers one is describing a temperament rather than a hierarchy.
The comparison in full is in Teutonic Thrash vs Bay Area Thrash, and the label that made the German scene possible is Noise Records.
The fourth cause: no competition to be melodic
One more mechanism, and it is about who each scene was playing to.
A Bay Area band in 1985 was competing with a dozen other bands in the same clubs, in front of an audience that had heard all of them, and the way to stand out in that market was to be better: tighter, more melodic, more sophisticated. The competitive pressure ran towards musicianship.
A band in Gelsenkirchen was competing with two other bands in the whole country, in front of an audience that had almost nothing else, and the way to stand out was to be more extreme. The competitive pressure ran the other way entirely.
Neither scene chose its direction. Both were responding to who was in the room.
What it produced downstream
The consequence is the most important fact in this article and it is rarely stated. American thrash produced better thrash. German thrash produced two other genres.
The rasped vocal, the tremolo picked figure, the deliberate primitivism and the refusal of melody are all present in the German records of 1985 and 1986, and death metal and black metal were built out of them. Florida and Norway have said so in print, repeatedly and without prompting.
That is a considerably larger legacy than being the best at your own genre, and it came from having worse access to the records everybody else was learning from. The full account is in Teutonic Thrash.
The one American exception
Slayer, and it is worth addressing because it complicates the tidy version above.
Everything said here about German riff writing applies to Reign in Blood: no resolution, no relief, chromatic figures, atonal leads. Slayer are temperamentally closer to Kreator than to any of their Bay Area contemporaries, and they arrived there independently, from southern California, with full access to the same records the East Bay had.
So the reference library is not deterministic. It is a very strong tendency with one significant counterexample, and the counterexample is the most extreme American band of the period, which suggests the causation runs through temperament as much as through what was in the record shop.
Sources and notes
Years and labels refer to original pressings. Attributions of influence follow the musicians' published statements.