Both, I have several guitars set up with a low action for shred but if I was to play slide at all I would definitely have one of them set up with a higher action, like on my acoustic.
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I like it as low as possible without buzzing AT ALL when unplugged, which is about 2.3-5mm on my low e..
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Generally,low action is much easier to play.
Current situation:
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Low because I like making large bends and sliding a lot (not with a slide).
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Alright, I'll give them a try, Japanese Black Speed rarely disappoints.

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Hmm judging from your pic you'd fit in more with a fat busted tribute.
High, with the pickups as close as possible.
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Rather low because I need it to be low to get my pickups close enough - but not so low that I've got no sustain. You'll want to find your middle-ground, unless you're not going to play anything that requires sustain whatsoever.
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I keep my guitar's action at about 6/64ths bass-side from the 8th fret on. It starts at about 4/64ths at the first few frets for chording.