"I should not copy him exactly, to avoid getting overlapping our spectrum ranges"
What about double-tracked guitars on pretty much ever modern rock album? Sometimes the tones are divergent, but often its the EXACT same tone, just a different take. When you pan L/R you get stereo separation and there's no "fighting", but a synergy of tone! I don't know how you run everything live, but I don't think there's a real danger of having a very similar tone as your fellow guitarist.
It's nice to have different tones so you can more clearly each guitar, but unless they're both panned dead center, I wouldn't worry about frequency overlap.
Also, make sure to try small (+/- 0.2) adjustments to high and low shift on the cab profile. These can have some pretty large effects on the tone that you can't get via EQ.