I'm looking to buy some new pickups for my Ibanez (two humbuckers). Specifically I'm looking at Seymour Duncans because my Dad has some work connections and can get them for cheap. I was originally going to go for a '59 in my neck position and a JB in my bridge, but a friend told me to go for a '59 and a Pearly Gates. I've also heard good things about the Jazz model.

Mostly I play blues and rock. I'm really big into Led Zeppelin, Pink Floyd, and stuff like RHCP, Muse, Sabbath, The Who, but also I play The Beatles and Stones quite frequently too. What would be the ideal choice for me?
Can only comment on what I have which is JB/59 combo and I really like it. Perhaps look at a pair of 59's too (which is what my teacher uses)
I perfer the '59 in both position since you can get the dirt that you need with having cleanes as well.
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Pearly gates in the bridge, 59 in the neck.
Then there's this band called Slice The Cake...

Bunch of faggots putting random riffs together and calling it "progressive" deathcore.
Stupid name.
Probably picked "for teh lulz"

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Firstly, what's your amp, what's wrong with your current tone and how do you think it could be improved? Don't start thinking about specific pickup models until you've gone through those three questions.

Though for what it's worth and to get it out the way, you can't really go wrong with any kind of 59/Jazz/JB model combination. The main choice is how much output you want in the bridge, if you want a lot you got for the JB otherwise you go for the 59 in the bridge and either the Jazz or 59 works fine int he neck. The main tonal differencse between the 59 and Jazz is the Jazz is a little clearer-sounding and ever so slightly lower output, but ultimately you can have either in either position and they're equally good. I'd merely suggest you pick the Jazz if your guitar is naturally darkly-toned, or you pick the 59 if it's a naturally brighter instrument.

The Pearly Gates isn't bad either but I think a JB/Jazz/59 selection would generally be better. The Pearly Gates is a little inbetween the 59 and JB models to my ears, it tries to be hotter while retaining clarity and that just doesn't work out for me, I think you're better off dedicating yourself to one of the others than going with the jack-of-all-trades Pearly Gates.
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For the types of tone you want I'd go for the Seth Lover (SH-55) set if you can get them for cheap.
I personally like a JB in the bridge. They distort well but not over the top. And it cleans up real nice. It has a nice warm tone. I've got one in every guitar I own. As for the neck, a 59 is great as is the Jazz. They're both pretty close in sound, but the 59 is a little more raw. To my ear, the Pearly Gates sounds like a beefed up single coil. I had one once and didn't really care for it.
There's my way and the wrong way.