I'd go with the one that feels right. The tone will change over time through playing technique, different amps, even simple "mods" to the bass a bit (new strings, different pickups, etc).
If the bass seems too heavy, then consider getting a very comfortable strap (preferably a thicker strap).
Not that my experiences should fully sway your choice, but my first bass is an Ibanez EX-404 (P/J). I still use it for many styles of music: jazz, funk, metal, pop songs. The tone and volume knobs don't even turn anymore, I just use the Blend knob (sometimes) and change my playing technique (lighter/heavier plucking, pluck near the neck or the bridge). Currently it has very bright strings, so I designate that bass for more pop-funk-rock situations nowadays.
I'd concentrate more on technique and the love of playing music than worrying about the finer details of tone. Over time you'll figure out what you can do and what you want to hear from your gear in a band setting.