Yeah, what are the pros and cons of a brass nut? I have a Spector NS-2000/Q5 and saw that the NS-2000/5 has a brass nut and got curious.
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Brass nuts are definitely more durable in the long run. On open notes, they allegedly sound brighter than other material.

However, the one bass I have that has one is finicky with the tuning. Don't know if its the bass or the nut that is the cause.
Pros: Open strings have the same tone as a fretted note.

Cons: Can't be adjusted easily.
Wood doesn't affect tone, leave the rainforest alone..
Brass nuts will probably enhance sustain, in another life many years ago our steel guitarist used a solid brass slide.
G&L L2500
Squier Affinity Jazz Bass 5
Ashdown RPM pre-amp
Ashdown Little Giant 1000
300 watt 15" powered cab
450 watt 15" powered sub bass cab
2x10 + horn
1x15x10 + horn