#1
I'm a guitarist looking to play some bass and I own an axl badwater guitar and really like it, I see that they also sell basses now but there's a catch, you have to choose between 1 split pickup or 1 split pick up + a single coil. So the question is, what's the advantage of having the extra single coil instead of just the split, and what exactly is the characteristics of both types. I ask because I know on guitar the bridge/neck pickups differ greatly in sound but wanted to know what the diff. is on bass. Here's a link to check it out.

http://www.axlguitars.com/ap820br.html
#2
The single split coil is pretty versatile, and will get you a good amount of sounds anywhere from Punk and Metal, like Mike Dirnt or the guy from Anti-Flag to more mellow, fat sounds. The two pickup bass is even more versatile, and can get you the above sounds as well as sounds similar to Frank Bello of Anthrax, even maybe to Marcus Miller or Flea style slap/pop sounds or Jaco Pastorious' mid-heavy jazz sound.
#3
Split coils are semi humbucking, and give a more thumpy, rounder sound. They are most commonly seen on Precision basses.

The singe coils generally have a brighter, more clear tone. Often seen on jazz basses, though obviously in this case, you just get the bridge pickup.

Neck and bridge positioning has the same effect as on guitar. Neck is warmer, while bridge is brighter.

Personally, I would go with the combination one. Even if you don't like its tone, you can just turn it off, and you have exactly what you would otherwise have. Versitility is never a bad thing.
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+1