So there's a sale at my local music shop where everything's going at 50%
I've come up with a couple of basses to get.

Ibanez RD500 (or something along the series)
Ibanez SDX590 (they seem to only have 595, which is 5 strings. So i dunno if they have stock + I love the colour)
Ibanez lcb 300
Fender Jazz bass (Deluxe maybe?)

I currently have a ibanez gsr 190.

I'd appreciate if someone gave me the run down on the models.

I play mostly rock/alternative stuff.
Almost never slap/pop.
So yeah, i like a more bassy sound.
Wouldn't go with a jazz bass, for rock and alternative the Ibanezs are the best, the SDX590 are exactly the same sounding as their 4 string coutnerpart, you're just paying an extra 25% to be able to go half an tad higher.
i'd take the jazz bass if you like how it feels.

jazz basses sound good in any situation and i use one in my rock band, my metal band and my blues band
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The only bass I would immediately avoid in the series is the ICB. Caveat--I have never played one, but I have never heard an Ibanez fan boy / girl who liked that bass. Yes, they may look cool but they are allegedly hard to play and have an odd tone.

Which leaves your Fender Jazz and SR series Ibanez. Hmm..

Since you have a bass already, the 5er would be a nice second bass. If you slap a decent amount, make sure you put the Ibanez through its paces. The distance between the strings on the Ibanez 5ers is a bit tight compared to other 5ers.

If you are looking between the remaining Ibanez and the Fender, its going to come down to preference about bass necks, available frets and sound. Both are good basses, but in this comparison I'd probably lean a bit towards the Jazz.
I'd vote Ibanez. Preferably the 5er: the extra depth will come in handy for your style. You'd really need an active J (IMO of course ) to be anywhere near.

Think what your favourite bassists play, if you want another perspective.