I think that the tone wood is more important than what pickups come with a guitar - you can always replace pickups (and I always do).
In my experience, having owned both guitars with agathis and basswood, I love basswood. It's light, it has an overall pretty bright and present sound, which means that it cuts through the mix and doesn't kill my back. Pretty important, to me. Construction does impact tone - I have a Jackson that is made from basswood, but has very little bass, while the LTDs that I own are also basswood but have a pretty respectable low end.
My second guitar was a BC Rich Warlock (platinum series), and I grew to despise it. The hardware was soft, so the saddle developed burrs, the pickups were dark and muddy (could barely hear the high E string, so couldn't solo for crap), and because it didn't have a fixed bridge (it had one of those trems where you can go down in pitch but not up... forget what they're called...) it didn't want to stay in tune for very long. Not good times. It didn't even sound that good after I put EMGs in it!
I came to the realization that agathis is a pretty crappy tone wood, at least in the lower price point guitars. Basswood used to be the same way, actually, but the more popular it grew the better the quality became. The least I can say is that the agathis used in my BC Rich was crap - very little sustain, and an overall "dull" sound to it, without that rich mahogany fundamental presence that makes mahogany sound so frickin' awesome. So dull, not warm.
For high gain stuff, the only really two contributing factors that tone wood offers is sustain and overall balance between treble and bass.... and you can even out a skewed balance with the right pickups. Pickups and the right amp are far more important, to me, even than the tone wood, for high gain rock/metal.
Anyways, my vote would be for the Ibanez, even though I don't like the floating tremolo. It will go out of tune faster than a fixed bridge, you won't be able to retune it without re-setting it up again, and if you snap a string the whole guitar will need to be re-adjusted, all of the strings will go out of tune.
Floating trems are a PITA, and I intensely dislike them. I want my guitar to stay in tune, and even a pretty decent Floyd Rose (which the lower priced Edge III trems certainly are *not*) will go out of tune faster than a well-adjusted fixed bridge guitar.
Plus, its harder to set up a floating trem guitar if you use thick strings - and I really *really* like using thicker strings (ie 11's).
Anyways, that's my two cents. I think its better to buy a 200$ guitar and put 150$ worth of pickups in it than to buy a 350$ guitar and leave it stock - I'm big on customization, and I swear that the right pickups can make even a weak guitar sound 10x better!
Either way... play before you buy... good luck!
Saul