Chula Vista

Speaking from a "majority of the time" standpoint:

In which genres does the bassist pretty much follow the guitars both melodically and rhythmically?

And in which genres is the bassist more independant to compliment and weave around what the guitars are doing?

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Frownland

Funk metal is probably the most syncopated genre. Maybe symphonic proggressive metal as well?

Death metal and black metal are good contenders for the other one.

Wpnfire

In like 90% of metal, the bassist is playing the same riffs as the guitars, except where the guitars are playing notes the bass can’t hit, in which case it will be a variation of the riff.

The other 10% of the time it’s like technical death metal where the bassist could be playing its own thing. I’m not to sure about that though. Overwhelmingly across all metal genres the bass is playing the riff though.

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MicShazam

I tend to listen for the bass a lot in all forms of music so I notice how boring it is in most metal genres.

Some heavy metal has the bass play steady notes while the riffs weave around. Kind of like Iron Maiden, where Steve Harris' bass gallops while the guitars may play some other rhythm. Death metal strikes me as the genre where there's least to listen to in general.

I'd say you can find plenty of individual bands where the bass is doing it's own thing, but on genre level, I don't think any metal genre is good with letting the bass player do anything of his/her own.

I could mention bands that have more room for bass playing than most, but that's not what you asked. So basically, I'm sticking with heavy metal as the most bass friendly metal genre. Possibly power metal too, but I'm not sure since I don't listen to much in that genre.

EDIT: Nu metal bass players might also generally play what the guitars do, but I love how they at least tend to be mixed pretty loud compared to other metal genres.